Option 2

Task B1.

A weight of mass 2 kg is suspended on a thin cord. If it is deflected from the equilibrium position by 10 cm and then released, it oscillates freely like a mathematical pendulum. What will happen to the period of oscillation of the weight, the maximum potential energy of the weight and the frequency of its oscillations if the initial deviation of the weight is 5 cm?

Since the period of a mathematical pendulum is determined by the formula:

A frequency

That is, do not depend on the amplitude of the oscillations, then the period and frequency of the oscillations will not change.

The potential energy will decrease, because the smaller the amplitude, the lower the weight rises to a lower height -
.

Physical quantities. Their change.

A) period 1) will increase

B) frequency 2) will decrease

C) maximum potential 3) will not change

Task B2.

The stone freely falls vertically down. Do the physical quantities listed in the first column change during its downward movement, and if so, how? Establish a correspondence between the physical quantities listed in the first column and the possible types of their changes listed in the second column. Ignore the effect of resistance.

Physical quantities. Their changes.

A) speed 1) does not change

B) acceleration 2) increases

C) kinetic energy 3) decreases.

D) potential energy

Explanation. The speed of the body when moving down increases, since the force of gravity is directed along the movement. The acceleration remains constant because .

Kinetic energy is determined by the formula
, so as the speed increases. Potential energy is determined by the formula
, so it decreases. Answer:

Task B3.

The temperature of a small lead ball when falling on a massive steel plate increased by 1 0 C. Neglecting the energy losses for heat transfer to surrounding bodies. Determine the height from which the ball fell from the result of this experiment. The specific heat capacity of lead is 130 J/(kg∙K). Acceleration of free fall is taken equal to

10 m/s 2 . Write your answer as a number expressed in meters.

Since at a height h the body has potential energy, determined by the formula, and for heating the body, the heat
, then according to the law of conservation of energy

From here we get:

;

Answer: 13m.

Task B4.

Calculate the current in the circuit when connected to a 12 V DC source with an internal resistance of 2 ohms and a resistor with an electrical resistance of 4 ohms. Write your answer as a number expressed in amperes.

According to Ohm's law for a complete circuit, the current strength is determined by the formula:

, we get

Answer: 2A.

Task B5.

The focal length of the converging lens is 15cm. At what distance from the lens is an object whose actual image was obtained at a distance of 60 cm from the lens? Write your answer as a number expressed in centimeters.

According to the thin converging lens formula, we have:

, from here we get:
, let's plug in the data:

d=20cm

Answer: 20 cm

Task C1.

The experiment found that when the air temperature in the room is 25 0 C, condensation of water vapor from the air begins on the wall of the glass with cold water, if the temperature of the glass is reduced to 14 0 C. Based on the results of these experiments, determine the absolute and relative humidity of the air. Use the table to solve the problem. Will the relative humidity change with an increase in the air temperature in the room, if the condensation of water vapor from the air begins at the same glass temperature of 14 0 C. Pressure and density of saturated water vapor at different temperatures.

The relative humidity of the air is determined by the formula:

%,

where p is the partial pressure, P 0 is the saturated vapor pressure, which at a given temperature is taken from the table. The partial pressure in the condition of this problem is taken from the table at the temperature at which vapor condensation begins. We get P 0 \u003d 3200 Pa, p \u003d 1600 Pa.

Hence, the humidity of the air is:

As the temperature rises, the saturated vapor pressure will increase, while the partial pressure will not change, since condensation occurs at the same temperature. Therefore, the relative humidity in this case will decrease.

Task C2.

In the attraction, a person weighing 60 kg moves on a trolley along rails and makes a "dead loop" in a vertical plane along a circular path with a radius of 5 m. What is the pressure force of a person on the seat of the trolley at a speed of passing the bottom point of 10m/s? Acceleration of free pressure is taken equal to 10m/s 2 .

Solution: we will depict in the drawing the trajectory of movement and the forces acting on the person at the top point:

According to Newton's second law, the vector sum of forces acting on a body is equal to the product of mass and acceleration:

,

in scalar form, this equation has the form:

,

where F T \u003d mg: from here we find the reaction force of the support: N \u003d mg + ma. Since the centripetal acceleration is determined by the formula:
, then we get the formula: N=m (g+v 2 /R).

Substitute the data and do the calculations: N=60 (10+100/5) =1800H

According to Newton's third law, the force of a person's pressure on the seat is equal in absolute value to the reaction force of the support, i.e. F d \u003d N, F d \u003d 1800H

Answer: 1800N.

Task C3.

The diagram shows the changes in pressure and volume of an ideal monatomic

gas. How much heat was received or given away by the gas during the transition from state 1 to state 3?

The total amount of heat is determined by the formula:

Q 123 \u003d Q 12 + Q 23

Q 12 \u003d A 12 + ΔU 12 'where A 12 \u003d P ΔV \u003d 0

ΔU=3/2νRΔT=3/2V 1 (P 2 -P 1)

then the amount of heat in section 1-2 will be equal to:

Q 12 \u003d 3 / 2 1 ∙ (10-30) \u003d -30 kJ.

The amount of heat in section 2-3 will be equal to:

Q 23 \u003d A 23 + ΔU 23; Q 23 \u003d P 2 (V 3 -V 2) + 3 / 2P 2 (V 3 -V 2) \u003d

5 / 2P 2 (V 3 -V 2); Q=5/2∙10∙(3-1)=50 kJ,

then the total amount of heat will be: Q=-30+50=20kJ

Heat will be received.

Answer: 20 kJ.

Task C4.

The cathode of a photocell with a work function of 4.42∙10 -19 J is illuminated by light with a frequency

1.0∙10 15 Hz. The electrons emitted from the cathode fall into a uniform magnetic field with an induction of 8.3∙10 -4 T perpendicular to the lines of induction of this field. What is the maximum radius of the circle R along which the electrons move?

According to the law of conservation of energy for the photoelectric effect, we have the formula:

hν = Aout + E k , E k =mv 2 /2, then hν=Aout + mv 2 /2.

From here we determine the speed of the electron:

In a magnetic field, a charged particle is affected by the Lorentz force, which is determined by the formula: F=qvBsinα, since the angle is 90 0 C, then sinα=1, then F=qvB.

According to Newton's second law, the force is F=ma.

Equating the two formulas, we obtain the equality: qvB=ma. Acceleration is determined by the formula: a=v 2 /R, hence qvB=m v 2 /R, simplifying, we get:

R \u003d mv / qB, substituting the data, we will perform the calculations:

R=9.1∙10 -31 ∙6.92∙10 5 / (1.6∙10 -19 ∙8.3∙10 -4) =4.74∙10 -3 m=4.74mm

Answer: 4.74 mm.

Task C5.

A 4 m deep pool is filled with water, the relative refractive index at the air-water boundary is 1.33. What does the depth of the pool appear to be to an observer looking vertically down into the water?

According to the law of refraction
, where is the refractive index of water, 1 is the refractive index of air. From the triangles ABC and MBC we find the leg x: x=h tgβ, x=H∙tgα. Since the left parts are equal, so the wounds and the right parts, we get the equation: h∙ tgβ= H∙ tgα, hence h= H∙ tgα/ tgβ. Angles α and β are taken very small, therefore sinα= tgα, sin β= tgβ. We get the equality:

h=H sinα/ sin β =H/n, we get: h=4/1.33=3 m.

Answer: 3 m.

Task C6.

Using tables of masses of atomic nuclei and elementary particles, calculate the energy released during the synthesis of 1 kg of helium from hydrogen isotopes - deuterium and tritium:

Masses of atomic nuclei

	Name element		Mass of the atomic nucleus of an isotope
			1, 6726∙10 -27 kg	1, 00727 a. eat.
			3, 3437∙10 -27 kg	2.01355a. eat.
			5, 0075∙10 -27 kg	3.01550 a. eat.
			5.0066∙10 -27 kg	3.01493a. eat.
			6.6449∙10 -27 kg	4.00151a. eat.
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Solving problems in physics.

Training tasks of the Unified State Examination of the level "B" and "C" in 2010.

Option 1

Task number B1.

A weight of mass 2 kg is suspended from a long thin cord. If it is deflected from the equilibrium position by 10 cm, and then released, it oscillates freely like a mathematical pendulum with a period of 1 s. What will happen to the period, the maximum potential energy of the weight and the frequency of its oscillations if the initial deviation of the weight is 20cm?

A frequency

Those. do not depend on the amplitude of the oscillations, then both the period and the frequency of the oscillations will not change.

The potential energy will increase, because the greater the amplitude, the greater the height of the weight rises -.

A) period 1) will increase

B) frequency 2) will decrease

C) maximum potential 3) energy will not change.

BUT	B	AT
3	3	1

Task number B2.

A stone is thrown vertically upwards. Do the physical quantities listed in the first column change during its upward movement, and if so, how? Ignore the effect of air resistance.

A) speed 1) does not change

B) acceleration 2) increases

D) potential energy

Explanation. The speed of the body when moving up decreases, since the force of gravity is directed opposite to the movement. The acceleration remains constant because

Kinetic energy is determined by the formula, therefore, as well as the speed decreases.

Potential energy is determined by the formula, so it increases.

BUT	B	AT	G
3	1	3	2

Task B3.

The temperature of a small lead ball when falling onto a massive steel plate from a height of 6.5 m increased by 0.5 0 C. Neglecting the energy loss for heat transfer to surrounding bodies, determine the specific heat capacity of lead from the result of this experiment. Acceleration of free fall is taken equal to 10m/s 2 .

From here we get:

Answer: 130 J/kg K.

Task B4.

Calculate the current in the circuit when connected to a DC source with an EMF of 6 V and an internal resistance of 1 Ω of a resistor with an electrical resistance of 2 Ω. Write your answer as a number expressed in amperes.

We get

Answer: 2A.

Task B5.

The focal length of the converging lens is 15 cm. At what distance from the lens is the image of an object located at a distance of 20 cm from the lens? Write your answer as a number expressed in centimeters.

1/60; f=60cm

Answer: 60 cm

Task C1.

The experiment found that when the air temperature in the room is 23 0 C, condensation of water vapor from the air begins on the wall of the glass with cold water, if the temperature of the glass is reduced to 12 0 C. Based on the results of these experiments, determine the absolute and relative humidity of the air. Use the table to solve the problem. Explain why the condensation of water vapor in air can begin at different temperatures. Pressure and density of saturated water vapor at different temperatures.

t 0 C	7	9	11	12	13	14	15	16
PgPa	10	11	13	14	15	16	17	18
ρ g/m 3	7,7	8,8	10,0	10,7	11,4	12,11	12,8	13,6
t 0 C	19	21	23	25	27	29	40	60
P hPa	22	25	28	32	36	40	74	200
ρ g/m 3	16,3	18,4	20,6	23	25,8	28,7	51,2	130,5

We determine the relative humidity of the air by the formula:%, where p is the partial pressure, P 0 is the pressure of saturated steam, which at a given temperature we take from the table. The partial pressure in the condition of this problem is taken from the table at the temperature at which vapor condensation begins. We get P 0 \u003d 3200 Pa, p \u003d 1400 Pa.

The absolute humidity of the air is equal to the vapor density at a given temperature, i.e. 20.6 g / m 3, or can be considered equal to the partial pressure at this temperature, which is equal to the saturated vapor pressure at the condensation temperature. Condensation of water vapor in the air can begin at different temperatures due to the fact that the relative humidity is different. With a higher relative humidity, the concentration of water vapor in the air is greater, therefore, at a higher temperature, this water vapor will become saturated, i.e. Condensation will start at a higher temperature than when the relative humidity is lower.

Task C2.

In the attraction, a person weighing 70 kg moves on a trolley along rails and makes a "dead loop" in a vertical plane. With what speed does the trolley move at the top point of a circular trajectory with a radius of 5 m, if at this point the pressure force of a person on the trolley seat is 700 N? Acceleration of free pressure is taken equal to 10m/s 2 . Solution: we will depict in the drawing the trajectory of movement and the forces acting on the person at the top point: According to Newton's second law, the vector sum of the forces acting on the body is equal to the product of mass and acceleration:

In scalar form, this equation has the form:

Where F T \u003d mg: from here we find the acceleration:

Since the centripetal acceleration is determined by the formula: , then we get the speed formula:

.

Answer: 10m/s.

Task C3.

The diagram shows changes in pressure and volume of an ideal monatomic gas. How much heat was received or given away by the gas during the transition from state 1 to state 3?

Q 123 \u003d Q 12 + Q 23

Q 12 \u003d A 12 + ΔU 12 'where A 12 \u003d PΔV \u003d P 1 (V 2 -V 1),

then the total amount of heat will be equal to: Q 123 =50+90=140kJ. Heat will be received.

Answer: 140 kJ.

Task C4.

With a short circuit of the battery terminals, the current in the circuit is I 1 \u003d 12 A.

When connected to the battery terminals of an electric lamp with an electrical resistance of 5 ohms, the current in the circuit is I 2 \u003d 2A. Based on the results of these experiments, determine the emf of the generator.

According to Ohm's law for a complete circuit in the event of a short circuit, where r is the resistance of the current source. The external resistance in this case is 0.

If the external resistance is different from 0, then Ohm's law for a complete circuit is:

Expressing from two equations, we obtain a system of equations:

then the EMF of the source will be equal to:

Substituting the data, we get:

. Answer: 12V.

Task C5.

A mosquito flies near the surface in the river, a flock of fish is located at a distance of 2 m from the surface of the water. What is the maximum distance to a mosquito at which it can still be seen by fish at this depth? The relative refractive index of light at the air-water interface is 1.33.

Let's depict the location of a flock of fish and a mosquito on the surface of the water: At point A there are fish, at point B - a mosquito. According to the law of refraction, we have the formula: , where is the refractive index of water, for air the refractive index is 1. In order for the fish to see a mosquito, the angle of refraction must be equal to 90 0 . For the angle, by definition of the sine, we have:

Then, to determine the distance r, we obtain the formula:

Answer: 2.66m.

Task C6.

The photoelectric effect from the surface of this metal is observed at a radiation frequency of at least 6∙10 14 Hz. Find the frequency of the incident light if the photoelectrons emitted from the surface of the metal are completely trapped by the grid, the potential of which relative to the metal is 3V.

According to the law of conservation of energy for the photoelectric effect, in the case of light incidence with a frequency corresponding to the red border of the photoelectric effect and for a higher frequency, we obtain two equations:

, (1) and . (2)

Since the work of an electric current in moving a charged particle is equal to the change in the kinetic energy of this particle, i.e.

we obtain the second equation for the photoelectric effect in the form:

. (2)

Subtracting the first equation from the second equation, we get:

Plug in the data and do the calculations:

Answer: 1.3∙10 15 Hz.

Option 2

Task B1.

A weight of mass 2 kg is suspended on a thin cord. If it is deflected from the equilibrium position by 10 cm and then released, it oscillates freely like a mathematical pendulum. What will happen to the period of oscillation of the weight, the maximum potential energy of the weight and the frequency of its oscillations if the initial deviation of the weight is 5 cm?

Since the period of a mathematical pendulum is determined by the formula:

A frequency

That is, do not depend on the amplitude of the oscillations, then the period and frequency of the oscillations will not change.

The potential energy will decrease, because the smaller the amplitude, the lower the weight rises to a lower height -.

Physical quantities. Their change.

A) period 1) will increase

B) frequency 2) will decrease

C) maximum potential 3) will not change

BUT	B	AT
3	3	2

Task B2.

The stone freely falls vertically down. Do the physical quantities listed in the first column change during its downward movement, and if so, how? Establish a correspondence between the physical quantities listed in the first column and the possible types of their changes listed in the second column. Ignore the effect of resistance.

Physical quantities. Their changes.

A) speed 1) does not change

B) acceleration 2) increases

C) kinetic energy 3) decreases.

D) potential energy

Explanation. The speed of the body when moving down increases, since the force of gravity is directed along the movement. The acceleration remains constant because .

Kinetic energy is determined by the formula, so as the speed increases. Potential energy is determined by the formula, therefore, decreases. Answer:

BUT	B	AT	G
2	1	2	3

Task B3.

The temperature of a small lead ball when falling on a massive steel plate increased by 1 0 C. Neglecting the energy losses for heat transfer to surrounding bodies. Determine the height from which the ball fell from the result of this experiment. The specific heat capacity of lead is 130 J/(kg∙K). Acceleration of free fall is taken equal to

10 m/s 2 . Write your answer as a number expressed in meters.

Since at a height h the body has potential energy, determined by the formula, and heat for heating the body, then according to the law of conservation of energy

From here we get:

Answer: 13m.

Task B4.

Calculate the current in the circuit when connected to a 12 V DC source with an internal resistance of 2 ohms and a resistor with an electrical resistance of 4 ohms. Write your answer as a number expressed in amperes.

According to Ohm's law for a complete circuit, the current strength is determined by the formula:

We get

Answer: 2A.

Task B5.

The focal length of the converging lens is 15 cm. At what distance from the lens is an object whose actual image was obtained at a distance of 60 cm from the lens? Write your answer as a number expressed in centimeters.

According to the thin converging lens formula, we have:

From here we get: , we substitute the data:

d=20cm

Answer: 20 cm

Task C1.

The experiment found that when the air temperature in the room is 25 0 C, condensation of water vapor from the air begins on the wall of the glass with cold water, if the temperature of the glass is reduced to 14 0 C. Based on the results of these experiments, determine the absolute and relative humidity of the air. Use the table to solve the problem. Will the relative humidity change with an increase in the air temperature in the room, if the condensation of water vapor from the air begins at the same glass temperature of 14 0 C. Pressure and density of saturated water vapor at different temperatures.

t 0 C	7	9	11	12	13	14	15	16
PgPa	10	11	13	14	15	16	17	18
ρ g/m 3	7,7	8,8	10,0	10,7	11,4	12,11	12,8	13,6
t 0 C	19	21	23	25	27	29	40	60
P hPa	22	25	28	32	36	40	74	200
ρ g/m 3	16,3	18,4	20,6	23	25,8	28,7	51,2	130,5

The relative humidity of the air is determined by the formula:

where p is the partial pressure, P 0 is the saturated vapor pressure, which at a given temperature is taken from the table. The partial pressure in the condition of this problem is taken from the table at the temperature at which vapor condensation begins. We get P 0 \u003d 3200 Pa, p \u003d 1600 Pa.

Hence, the humidity of the air is:

As the temperature rises, the saturated vapor pressure will increase, while the partial pressure will not change, since condensation occurs at the same temperature. Therefore, the relative humidity in this case will decrease.

Task C2.

In the attraction, a person weighing 60 kg moves on a trolley along rails and makes a "dead loop" in a vertical plane along a circular path with a radius of 5 m. What is the pressure force of a person on the seat of the trolley at a speed of passing the bottom point of 10m/s? Acceleration of free pressure is taken equal to 10m/s 2 .

Solution: we will depict in the drawing the trajectory of movement and the forces acting on the person at the top point:

According to Newton's second law, the vector sum of forces acting on a body is equal to the product of mass and acceleration:

in scalar form, this equation has the form:

where F T \u003d mg: from here we find the reaction force of the support: N \u003d mg + ma. Since the centripetal acceleration is determined by the formula: , then we get the formula: N=m (g+v 2 /R).

Substitute the data and do the calculations: N=60 (10+100/5) =1800H

According to Newton's third law, the force of a person's pressure on the seat is equal in absolute value to the reaction force of the support, i.e. F d \u003d N, F d \u003d 1800H

Answer: 1800N.

Task C3.

The diagram shows the changes in pressure and volume of an ideal monatomic

gas. How much heat was received or given away by the gas during the transition from state 1 to state 3?

The total amount of heat is determined by the formula:

Q 123 \u003d Q 12 + Q 23

Q 12 \u003d A 12 + ΔU 12 'where A 12 \u003d P ΔV \u003d 0

ΔU=3/2νRΔT=3/2V 1 (P 2 -P 1)

then the amount of heat in section 1-2 will be equal to:

Q 12 \u003d 3 / 2 1 ∙ (10-30) \u003d -30 kJ.

The amount of heat in section 2-3 will be equal to:

Q 23 \u003d A 23 + ΔU 23; Q 23 \u003d P 2 (V 3 -V 2) + 3 / 2P 2 (V 3 -V 2) \u003d

5 / 2P 2 (V 3 -V 2); Q=5/2∙10∙(3-1)=50 kJ,

then the total amount of heat will be: Q=-30+50=20kJ

Heat will be received.

Answer: 20 kJ.

Task C4.

The cathode of a photocell with a work function of 4.42∙10 -19 J is illuminated by light with a frequency

1.0∙10 15 Hz. The electrons emitted from the cathode fall into a uniform magnetic field with an induction of 8.3∙10 -4 T perpendicular to the lines of induction of this field. What is the maximum radius of the circle R along which the electrons move?

According to the law of conservation of energy for the photoelectric effect, we have the formula:

hν=Aout + E k , E k =mv 2 /2, then hν=Aout + mv 2 /2.

From here we determine the speed of the electron:

In a magnetic field, a charged particle is affected by the Lorentz force, which is determined by the formula: F=qvBsinα, since the angle is 90 0 C, then sinα=1, then F=qvB.

According to Newton's second law, the force is F=ma.

Equating the two formulas, we obtain the equality: qvB=ma. Acceleration is determined by the formula: a=v 2 /R, hence qvB=mv 2 /R, simplifying, we get:

R \u003d mv / qB, substituting the data, we will perform the calculations:

R=9.1∙10 -31 ∙6.92∙10 5 / (1.6∙10 -19 ∙8.3∙10 -4) =4.74∙10 -3 m=4.74mm

Answer: 4.74 mm.

Task C5.

A 4 m deep pool is filled with water, the relative refractive index at the air-water boundary is 1.33. What does the depth of the pool appear to be to an observer looking vertically down into the water?

According to the law of refraction, where is the refractive index of water, 1 is the refractive index of air. From the triangles ABC and MBC we find the leg x: x=htgβ, x=H∙tgα. Since the left parts are equal, so the wounds and the right parts, we get the equation: h∙ tgβ= H∙ tgα, hence h= H∙ tgα/ tgβ. Angles α and β are taken very small, therefore sinα= tgα, sinβ= tgβ. We get the equality:

h=H sinα/ sin β =H/n, we get: h=4/1.33=3 m.

Answer: 3 m.

Task C6.

Using tables of masses of atomic nuclei and elementary particles, calculate the energy released during the synthesis of 1 kg of helium from hydrogen isotopes - deuterium and tritium:

Masses of atomic nuclei

Let's find the energy that is released during the synthesis of one nucleus according to the formula:

The number of nuclei contained in the mass of 1 kg of helium can be found by the formula:

Then the total energy will be equal to: E=E 1 ∙N; Plug in the data and do the calculations:

Е=1.5∙10 26 ∙0.2817∙10 -11 =4.2∙10 14 J

Answer: 4.2∙10 14 J

Literature

1. O.F. Kabardin, S.I. Kabardin "Typical test tasks", Publishing house "Exam", Moscow, 2010.

2. Yu.G. Pavlenko "The Beginnings of Physics", textbook, Exam Publishing House, Moscow, 2005.

3. G.Ya. Myakishev, B.B. Bukhovtsev "Physics, Grade 11", Moscow 2009 Publishing house "Enlightenment".

1 - The figure shows a graph of the dependence of the projection v x of the vehicle speed on time t. Which graph correctly represents the projection of the car's acceleration in the interval from time 4 s to 6 s?

2 - The figure shows the trajectory of a body thrown at some angle to the horizontal surface of the Earth. At point A of this trajectory, the direction of the velocity vector is indicated by arrow 1; the trajectory of the body and all vectors lie in a plane perpendicular to the surface of the Earth. Air resistance is negligible. What is the direction of the acceleration vector of the body in the Earth frame of reference? In your answer, indicate the number of the corresponding arrow.

3 - A person with a mass of 50 kg jumps from a stationary boat of mass 100 kg onto the shore with a horizontal speed of 3 m / s relative to the boat. With what speed does the boat move relative to the Earth after the jump of a person, if the resistance of water to the movement of the boat is negligible?

Answer: _____ m/s

4 - What is the weight of a person in water, taking into account the action of the force of Archimedes? The volume of a person is V = 50 dm 3, the density of the human body is 1036 kg / m 3.

Answer: _____ H

5 - In the experiment, a graph of the dependence of the velocity modulus of a rectilinearly moving body on time was obtained. Analyzing the graph, choose three correct statements from the statements below and indicate their numbers.

1 - The speed of the body in 6 seconds has changed from 0 m/s to 6 m/s.

2 - The body moved uniformly accelerated during the first 6 seconds and did not move in the interval from 6 to 7 seconds.

3 - The body moved uniformly in the first 6 seconds and did not move in the interval from 6 to 7 seconds.

4 - In the time interval of 4-6 seconds, the speed increased in direct proportion to the time of movement, the body moved with constant acceleration.

5 - The acceleration of the body at the fifth second of movement is 1.5 m/s2.

6 - A weight of 2 kg is suspended on a thin cord 5 m long. If it is deflected from the equilibrium position and then released, it oscillates freely, like a mathematical pendulum. What will happen to the period of the weight's oscillation, the maximum potential energy of the weight, and the frequency of its oscillations if the initial deviation of the weight is changed from 10 cm to 20 cm?

1 - increase

2 - decrease

3 - will not change

Write in the table the selected numbers for each physical quantity. Numbers in the answer may be repeated.

7 - A material point moves at a speed uniformly, rectilinearly and co-directionally with the coordinate axis OX. Establish a correspondence between physical quantities and formulas by which they can be calculated. For each position of the first column, select the corresponding position of the second and write down the selected numbers in the table under the corresponding letters.

8 - The graph shows how the temperature of 0.1 kg of water changed over time, which at the initial moment was in a crystalline state at a temperature of -100 0 С, at a constant heat transfer power of 100 W.

According to the graph in the figure, determine during what time the internal energy of water increased.

Decision

The graph shows that the temperature of the ice continuously increased and after 210 s it reached 0 0 C. Therefore, the kinetic energy of the ice molecules increased.

Then 333 s of ice transferred an amount of heat of 100 J every second, but the temperature of the melting ice and the resulting water did not change. The amount of heat 33300 J received during 333 s from the heater caused the complete melting of ice. This energy is used to break the strong bonds of water molecules in the crystal, to increase the distance between the molecules, i.e. to increase the potential energy of their interaction.

After all the ice melted, the process of heating the water began. The water temperature increased by 100 0 С in 418 s, i.е. the kinetic energy of the water has increased.

Since the internal energy is equal to the sum of the kinetic energy of all molecules and the potential energy of their interaction, the conclusion follows - the internal energy of water increased throughout the experiment for 961 s.

Answer: 961 s

9 - An ideal gas in some process shown in the graph did 300 J of work. How much heat was transferred to the gas?

Answer: _____ J

10 - In a closed room at an air temperature of 40 ° C, the condensation of water vapor on the wall of a glass of water begins when the water in the glass cools to 16 ° C.

What will be the dew point in this room if all the air in the room is cooled to 20 °C?

Answer: _____ °C

11 - Opposite electric charges are attracted to each other due to the fact that

1 - one electric charge is able to instantly act on any other electric charge at any distance

2 - around each electric charge there is an electric field that can act on the electric fields of other charges

3 - around each electric charge there is an electric field that can act on other electric charges

4 - there is a gravitational interaction

Which of the above statements is true?

Answer: _____

Decision :

Opposite electric charges are attracted to each other due to the fact that around each electric charge there is an electric field that can act on other electric charges.

Answer: 3

12 - In a physical experiment, the movement of a body on a horizontal and rectilinear section of the path from a state of rest was recorded for several seconds. According to the experimental data, graphs (A and B) of the time dependence of two physical quantities were plotted.

What physical quantities listed in the right column correspond to graphs A and B?

For each position of the left column, select the corresponding position of the right one and write down the selected numbers in the table under the corresponding letters.

Answer: _____

Decision :

On a horizontal section of the path, the position of the center of mass of the body does not change, therefore, the potential energy of the body remains unchanged. Answer 4 is excluded from the correct ones.

Answer 2 is excluded from the correct ones, because acceleration in uniformly accelerated motion is a constant value.

With uniformly accelerated motion from a state of rest, the path is calculated by the formula s= a* t 2 /2 . This dependence corresponds to graph B.

The speed during uniformly accelerated movement from a state of rest is calculated by the formula v= a* t. This dependence corresponds to graph A.

Answer: 13

13 - A positively charged particle A moves perpendicular to the plane of the figure in the direction towards the observer. Point B is in the plane of the figure. How is directed at point B (up, down, left, right, away from the observer, towards the observer) the induction vector of the magnetic field created by the moving particle A? Write your answer in word(s).

Answer: _____

Decision :

If we consider the movement of a positively charged particle as an electric current in a conductor that is perpendicular to the plane of the figure, then the gimlet (right screw) is directed along the current, and the rotation of the gimlet with respect to the observer will be counterclockwise. In this case, the lines of magnetic induction will be directed counterclockwise. Since the vector of magnetic induction of the magnetic field of the electric current coincides with the tangent to the line of magnetic induction, the vector of induction at point B is directed upwards.

Answer: up

14 - What is the voltage in the AB circuit section (see figure) if the current through a 2 ohm resistor is 2 A?

15 - The location of the flat mirror MN and the light source S is shown in the figure. What is the distance from the source S to its image in the mirror MN?

The location of the flat mirror MN and the light source S is shown in the figure. What is the distance from the source S to its image in the mirror MN?

Answer:_____

Decision :

The image of the light source in a flat mirror is located symmetrically with respect to the plane of the mirror. Therefore, the image in the mirror is exactly the same distance from the plane of the mirror as the light source.

Answer: 4 m

The graphs show the results of an experimental study of the dependence of the current strength on the voltage at the ends of the electric lamp filament and the resistance of the lamp filament on the current strength.

Analyzing the data, answer the question: what happened to the lamp in this experiment? Choose from the following two statements that correspond to the results of the experimental study.

1 - The lamp filament was heated by the flowing current, an increase in the temperature of the metal of the filament led to a decrease in its electrical resistivity and an increase in the resistance R of the lamp filament - graph R (I).

2 - The lamp filament was heated by the flowing current, an increase in the temperature of the metal of the filament led to an increase in its electrical resistivity and an increase in the resistance R of the lamp filament - graph R (I).

3 - The non-linearity of the dependences I(U) and R(I) is explained by too large measurement error.

4 - The results obtained contradict Ohm's law for the chain section.

5 - With increasing resistance of the lamp filament, the current through the lamp filament decreased - dependence I (U).

Answer: _____

Decision :

The filament of the lamp was heated by an electric current. As the temperature of a metal increases, its resistivity increases. Consequently, the resistance of the lamp filament increases. This causes the current through the lamp filament to decrease.

Answer: 25

17 - One electric lamp was connected to a direct current source, the electrical resistance of which is equal to the internal resistance of the current source. What will happen to the current in the circuit, the voltage at the output of the current source and the power of the current in the external circuit when a second such lamp is connected in series with this lamp?

For each value, determine the appropriate nature of the change:

1 - increase

2 - decrease

3 - immutability

Write in the table the selected numbers for each physical quantity. The numbers may be repeated.

18 - Graphs A and B show the dependence of some physical quantities on other physical quantities. Establish a correspondence between graphs A and B and the types of dependencies listed below. Write in the table the selected numbers under the corresponding letters.

1 - dependence of the number of radioactive nuclei on time

2 - dependence of stress on relative elongation

3 - dependence of the specific binding energy of nucleons in atomic nuclei on the mass number of the nucleus

4 - dependence of the magnetic field induction in the substance on the induction of the magnetizing field.

Decision :

Graph A shows the dependence of the number of radioactive nuclei on time (the law of radioactive decay).

Graph B shows the dependence of the specific binding energy of nucleons in atomic nuclei on the mass number of the nucleus.

Answer: 13

19 - As a result of a series of radioactive decays, U-238 turns into lead Pb-206. How many α-decays and β-decays does he experience in this case?

Answer: _____

Decision :

With each -decay, the charge of the nucleus decreases by 2, and its mass decreases by 4. During β-decay, the charge of the nucleus increases by 1, and the mass remains practically unchanged. Let's write the equations:

82=(92-2nα)+nβ

From the first equation: 4nα=32, the number of α-decays is 8.

From the second equation: 82=(92-16)+nβ=76+nβ,

82-76=nβ, 6=nβ, number of β-decays 6.

Answer: 8 6

20 - When a metal plate is illuminated with monochromatic light with a frequency ν, a photoelectric effect occurs. The maximum kinetic energy of the released electrons is 2 eV. What is the value of the maximum kinetic energy of photoelectrons when this plate is illuminated with monochromatic light with a frequency of 2v?

Answer: _____ eV

21 - With a very slow movement of the piston in the cylinder of a closed air pump, the air volume has decreased. How do pressure, temperature and internal energy of air change in this case? For each value, determine the corresponding nature of the change:

1 - increases

2 - decreases

3 - does not change

Write down the selected numbers for each physical quantity. Numbers in the answer may be repeated.

Decision :

With a very slow movement of the piston in the cylinder of a closed air pump, as a result of heat exchange with the environment, the air temperature in it does not change. With isothermal compression of a gas, the product of the pressure of the gas and its volume remains unchanged, therefore, with a decrease in the volume of air, its pressure increases. In an isothermal process, the internal energy does not change.

Answer: 133

22 - The figure shows a stopwatch, to the right of it is an enlarged image of the scale and arrow. The stopwatch hand makes a complete revolution in 1 minute.

Write down the stopwatch readings, taking into account that the measurement error is equal to the division of the stopwatch.

Answer: (____± ____) with

23 - In the experiment, the task was to determine the acceleration of the bar when sliding down an inclined plane of length l (1).

First, the formula for calculating the acceleration was obtained:

Then a detailed drawing was made with the dimensions of the inclined plane a (2), c (3) and the position of the force vectors and their projections.

Friction coefficient value μ (4) tree by tree the experimenter took from the reference data. Friction force F tr(5) and gravity mg(6) were measured with a dynamometer.

Which of the quantities marked with numbers is enough to use to determine the acceleration of the bar?

Decision :

The acceleration can be found knowing the coefficient of friction µ, the dimensions a, s,l inclined plane and calculating the values cosα= c/ l and sinα= a/ l.

Answer: 1234

24 - An ideal gas did 300 J of work, and at the same time, the internal energy of the gas increased by 300 J. How much heat did the gas receive in this process?

25 - A body with a mass of 2 kg under the action of a force F moves upward on an inclined plane at a distance l = 5 m, while the distance of the body from the Earth's surface increases by h = 3 m. The force F is 30 N. What work did the force F do during this movement ? Take the free fall acceleration equal to 10 m/s 2 , friction coefficient μ = 0.5.

Decision :

In the transition from the initial to the final state, the volume of the gas increases, therefore, the gas does work. According to the first law of thermodynamics:

The amount of heat transferred to the gas Q is equal to the sum of the change in internal energy for and the work done by the gas:

The internal energy of the gas in states 1 and 3 is expressed in terms of the pressure and volume of the gas:

The work during the transition of gas from state 1 to state 3 is equal to:

The amount of heat received by the gas:

A positive Q value means that the gas has received an amount of heat.

30 - When the battery terminals are short-circuited, the current in the circuit is 12 V. When an electric lamp with an electrical resistance of 5 ohms is connected to the battery terminals, the current in the circuit is 2 A. Based on the results of these experiments, determine the emf of the battery.

Decision :

According to Ohm's law for a closed circuit, when the battery terminals are short-circuited, the resistance R tends to zero. The current strength in the circuit is:

Hence, the internal resistance of the battery is:

When connected to the battery terminals of the lamp, the current in the circuit is equal to:

From here we get:

31 - A mosquito flies at the very surface of the water in the river, a flock of fish is at a distance of 2 m from the surface of the water. What is the maximum distance to mosquitoes at which it is still visible to fish at this depth? The relative refractive index of light at the air-water interface is 1.33.

The period of the mathematical pendulum. Kinetic and potential energy, specific heat capacity of lead. The current in the circuit when connected to a DC source. Relative humidity of the air, the amount of heat. Photoelectric effect from a metal surface.

Solving problems in physics.

Training tasks of the Unified State Examination of the level "B" and "C" in 2010.

Option 1 Task № B1. A weight of 2 kg is suspended on a long thin cord. If it is deflected from the equilibrium position by 10 cm, and then released, it oscillates freely like a mathematical pendulum with a period of 1 s. What will happen to the period, the maximum potential energy of the weight and the frequency of its oscillations if the initial deviation of the weight is 20 cm? Solution. Since the period of a mathematical pendulum is determined by the formula: do not depend on the amplitude of the oscillations, then the period and frequency of the oscillations will not change. The potential energy will increase, because the greater the amplitude, the greater the height of the weight rises -. Physical quantities. Their change. A) the period 1) will increase B) the frequency 2) will decrease C) the maximum potential 3) the energy will not change. Answer:

Task number B2.

A stone is thrown vertically upwards. Do the physical quantities listed in the first column change during its upward movement, and if so, how? Ignore the effect of air resistance.

A) speed 1) does not change

B) acceleration 2) increases

D) potential energy

Explanation. The speed of the body when moving up decreases, since the force of gravity is directed opposite to the movement. The acceleration remains constant because

Kinetic energy is determined by the formula, therefore, as well as the speed decreases.

Potential energy is determined by the formula, so it increases.

Task B3.

The temperature of a small lead ball when falling onto a massive steel plate from a height of 6.5 m increased by 0.5 0 C. Neglecting the energy loss for heat transfer to surrounding bodies, determine the specific heat capacity of lead from the result of this experiment. Acceleration of free fall is taken equal to 10m/s 2 .

Since at a height h the body has potential energy, determined by the formula, and heat for heating the body, then according to the law of conservation of energy From here we get:

Answer: 130 J/kg K.

Task B4.

Calculate the current in the circuit when connected to a DC source with an EMF of 6 V and an internal resistance of 1 Ω of a resistor with an electrical resistance of 2 Ω. Write your answer as a number expressed in amperes.

We get

Answer: 2A.

Task B5.

The focal length of the converging lens is 15 cm. At what distance from the lens is the image of an object located at a distance of 20 cm from the lens? Write your answer as a number expressed in centimeters.

Answer: 60 cm

Task C1.

The experiment found that when the air temperature in the room is 23 0 C, condensation of water vapor from the air begins on the wall of the glass with cold water, if the temperature of the glass is reduced to 12 0 C. Based on the results of these experiments, determine the absolute and relative humidity of the air. Use the table to solve the problem. Explain why the condensation of water vapor in air can begin at different temperatures. Pressure and density of saturated water vapor at different temperatures.

We determine the relative humidity of the air by the formula:%, where p is the partial pressure, P 0 is the pressure of saturated steam, which at a given temperature we take from the table. The partial pressure in the condition of this problem is taken from the table at the temperature at which vapor condensation begins. We get P 0 \u003d 3200 Pa, p \u003d 1400 Pa.

The absolute humidity of the air is equal to the vapor density at a given temperature, i.e. 20.6 g / m 3, or can be considered equal to the partial pressure at this temperature, which is equal to the saturated vapor pressure at the condensation temperature. Condensation of water vapor in the air can begin at different temperatures due to the fact that the relative humidity is different. With a higher relative humidity, the concentration of water vapor in the air is greater, therefore, at a higher temperature, this water vapor will become saturated, i.e. Condensation will start at a higher temperature than when the relative humidity is lower.

Task C2.

In the attraction, a person weighing 70 kg moves on a trolley along rails and makes a "dead loop" in a vertical plane. With what speed does the trolley move at the top point of a circular trajectory with a radius of 5 m, if at this point the pressure force of a person on the trolley seat is 700 N? Acceleration of free pressure is taken equal to 10m/s 2 . Solution: we will depict in the drawing the trajectory of movement and the forces acting on the person at the top point: According to Newton's second law, the vector sum of the forces acting on the body is equal to the product of mass and acceleration:

In scalar form, this equation has the form:

Where F T \u003d mg: from here we find the acceleration:

Since the centripetal acceleration is determined by the formula: , then we get the speed formula:

Answer: 10m/s.

Task C3.

The diagram shows changes in pressure and volume of an ideal monatomic gas. How much heat was received or given away by the gas during the transition from state 1 to state 3?

Q 123 \u003d Q 12 + Q 23

Q 12 \u003d A 12 + DU 12 "where A 12 \u003d RDV \u003d P 1 (V 2 -V 1),

then the total amount of heat will be equal to: Q 123 =50+90=140kJ. Heat will be received.

Answer: 140 kJ.

Task C4.

With a short circuit of the battery terminals, the current in the circuit is I 1 \u003d 12 A.

When connected to the battery terminals of an electric lamp with an electrical resistance of 5 ohms, the current in the circuit is I 2 \u003d 2A. Based on the results of these experiments, determine the emf of the generator.

According to Ohm's law for a complete circuit in the event of a short circuit, where r is the resistance of the current source. The external resistance in this case is 0.

If the external resistance is different from 0, then Ohm's law for a complete circuit is:

Expressing from two equations, we obtain a system of equations:

then the EMF of the source will be equal to:

Substituting the data, we get:

Answer: 12V.

Task C5.

A mosquito flies near the surface in the river, a flock of fish is located at a distance of 2 m from the surface of the water. What is the maximum distance to a mosquito at which it can still be seen by fish at this depth? The relative refractive index of light at the air-water interface is 1.33.

Let's depict the location of a flock of fish and a mosquito on the surface of the water: At point A there are fish, at point B - a mosquito. According to the law of refraction, we have the formula: , where is the refractive index of water, for air the refractive index is 1. In order for the fish to see a mosquito, the angle of refraction must be equal to 90 0 . For the angle, by definition of the sine, we have:

Then, to determine the distance r, we obtain the formula:

Answer: 2.66m.

Task C6.

The photoelectric effect from the surface of this metal is observed at a radiation frequency of at least 6 10 14 Hz. Find the frequency of the incident light if the photoelectrons emitted from the surface of the metal are completely trapped by the grid, the potential of which relative to the metal is 3V.

According to the law of conservation of energy for the photoelectric effect, in the case of light incidence with a frequency corresponding to the red border of the photoelectric effect and for a higher frequency, we obtain two equations:

Since the work of an electric current in moving a charged particle is equal to the change in the kinetic energy of this particle, i.e.

we obtain the second equation for the photoelectric effect in the form:

Subtracting the first equation from the second equation, we get:

Plug in the data and do the calculations:

Answer: 1.3 10 15 Hz.

Option 2 Task B1. A weight of 2 kg is suspended on a thin cord. If it is deflected from the equilibrium position by 10 cm and then released, it oscillates freely like a mathematical pendulum. What will happen to the period of oscillation of the weight, the maximum potential energy of the weight and the frequency of its oscillations, if the initial deviation of the weight is 5 cm? Solution. Since the period of a mathematical pendulum is determined by the formula: i.e. do not depend on the amplitude of the oscillations, then the period and frequency of the oscillations will not change. The potential energy will decrease, because the smaller the amplitude, the lower the weight rises to a lower height -. Physical quantities. Their change. A) period 1) will increase B) frequency 2) will decrease C) maximum potential 3) energy will not change. Answer:

Task B2.

The stone freely falls vertically down. Do the physical quantities listed in the first column change during its downward movement, and if so, how? Establish a correspondence between the physical quantities listed in the first column and the possible types of their changes listed in the second column. Ignore the effect of resistance.

Physical quantities. Their changes.

A) speed 1) does not change

B) acceleration 2) increases

C) kinetic energy 3) decreases.

D) potential energy

Explanation. The speed of the body when moving down increases, since the force of gravity is directed along the movement. The acceleration remains constant, since.

Kinetic energy is determined by the formula, so as the speed increases. Potential energy is determined by the formula, so it decreases. Answer:

Task B3.

The temperature of a small lead ball when falling on a massive steel plate increased by 1 0 C. Neglecting the energy losses for heat transfer to surrounding bodies. Determine the height from which the ball fell from the result of this experiment. The specific heat capacity of lead is 130 J/(kg K). Acceleration of free fall is taken equal to

10 m/s 2 . Write your answer as a number expressed in meters.

Since at a height h the body has a potential energy determined by the formula, and heat for heating the body, then according to the law of conservation of energy

From here we get:

Answer: 13m.

Task B4.

Calculate the current in the circuit when connected to a 12 V DC source with an internal resistance of 2 ohms and a resistor with an electrical resistance of 4 ohms. Write your answer as a number expressed in amperes.

According to Ohm's law for a complete circuit, the current strength is determined by the formula:

We get

Answer: 2A.

Task B5.

The focal length of the converging lens is 15 cm. At what distance from the lens is an object whose actual image was obtained at a distance of 60 cm from the lens? Write your answer as a number expressed in centimeters.

According to the thin converging lens formula, we have:

From here we get: , we substitute the data:

Answer: 20 cm

Task C1.

The experiment found that when the air temperature in the room is 25 0 C, condensation of water vapor from the air begins on the wall of the glass with cold water, if the temperature of the glass is reduced to 14 0 C. Based on the results of these experiments, determine the absolute and relative humidity of the air. Use the table to solve the problem. Will the relative humidity change with an increase in the air temperature in the room, if the condensation of water vapor from the air begins at the same glass temperature of 14 0 C. Pressure and density of saturated water vapor at different temperatures.

The relative humidity of the air is determined by the formula:

where p is the partial pressure, P 0 is the saturated vapor pressure, which at a given temperature is taken from the table. The partial pressure in the condition of this problem is taken from the table at the temperature at which vapor condensation begins. We get P 0 \u003d 3200 Pa, p \u003d 1600 Pa.

Hence, the humidity of the air is:

As the temperature rises, the saturated vapor pressure will increase, while the partial pressure will not change, since condensation occurs at the same temperature. Therefore, the relative humidity in this case will decrease.

Task C2.

In the attraction, a person weighing 60 kg moves on a trolley along rails and makes a "dead loop" in a vertical plane along a circular path with a radius of 5 m. What is the pressure force of a person on the seat of the trolley at a speed of passing the bottom point of 10m/s? Acceleration of free pressure is taken equal to 10m/s 2 .

Solution: we will depict in the drawing the trajectory of movement and the forces acting on the person at the top point:

According to Newton's second law, the vector sum of forces acting on a body is equal to the product of mass and acceleration:

in scalar form, this equation has the form:

where F T \u003d mg: from here we find the reaction force of the support: N \u003d mg + ma. Since the centripetal acceleration is determined by the formula: , then we get the formula: N=m (g+v 2 /R).

Substitute the data and do the calculations: N=60 (10+100/5) =1800H

According to Newton's third law, the force of a person's pressure on the seat is equal in absolute value to the reaction force of the support, i.e. F d \u003d N, F d \u003d 1800H

Answer: 1800N.

Task C3.

The diagram shows the changes in pressure and volume of an ideal monatomic

gas. How much heat was received or given away by the gas during the transition from state 1 to state 3?

The total amount of heat is determined by the formula:

Q 123 \u003d Q 12 + Q 23

Q 12 \u003d A 12 + DU 12 "where A 12 \u003d RDV \u003d 0

ДU=3/2нRDТ=3/2V 1 (P 2 -P 1)

then the amount of heat in section 1-2 will be equal to:

Q 12 \u003d 3/2 1 (10-30) \u003d -30 kJ.

The amount of heat in section 2-3 will be equal to:

Q 23 \u003d A 23 + DU 23; Q 23 \u003d P 2 (V 3 -V 2) + 3 / 2P 2 (V 3 -V 2) \u003d

5 / 2P 2 (V 3 -V 2); Q=5/2 10 (3-1)=50 kJ,

then the total amount of heat will be: Q=-30+50=20kJ

Heat will be received.

Answer: 20 kJ.

Task C4.

The cathode of a photocell with a work function of 4.42 10 -19 J is illuminated by light with a frequency

1.0 10 15 Hz. The electrons emitted from the cathode fall into a uniform magnetic field with an induction of 8.3 10 -4 T perpendicular to the lines of induction of this field. What is the maximum radius of the circle R along which the electrons move?

According to the law of conservation of energy for the photoelectric effect, we have the formula:

hn \u003d Aout + E k, E k \u003d mv 2 / 2, then hn \u003d A out + mv 2 / 2.

From here we determine the speed of the electron:

In a magnetic field, a charged particle is affected by the Lorentz force, which is determined by the formula: F=qvBsinb, because the angle is 90 0 C, then sinb=1, then F=qvB.

According to Newton's second law, the force is F=ma.

Equating the two formulas, we obtain the equality: qvB=ma. Acceleration is determined by the formula: a=v 2 /R, hence qvB=m v 2 /R, simplifying, we get:

R \u003d mv / qB, substituting the data, we will perform the calculations:

R=9.1 10 -31 6.92 10 5 / (1.6 10 -19 8.3 10 -4) =4.74 10 -3 m=4.74mm

Answer: 4.74 mm.

Task C5.

A 4 m deep pool is filled with water, the relative refractive index at the air-water boundary is 1.33. What does the depth of the pool appear to be to an observer looking vertically down into the water?

According to the law of refraction, where is the refractive index of water, 1 is the refractive index of air. From the triangles ABC and MBC we find the leg x: x \u003d h tgv, x \u003d H tgb. Since the left parts are equal, so the wounds and the right parts, we get the equation: h tgv \u003d H tgb, hence h \u003d H tgb / tgv. Angles b and c are taken very small, therefore sinb \u003d tgb, sin c \u003d tgv. We get the equality:

h \u003d H sinb / sin c \u003d H / n, we get: h \u003d 4 / 1.33 \u003d 3 m.

Answer: 3 m.

Task C6.

Using tables of masses of atomic nuclei and elementary particles, calculate the energy released during the synthesis of 1 kg of helium from hydrogen isotopes - deuterium and tritium:

Masses of atomic nuclei

	Name element		Mass of the atomic nucleus of an isotope
			1, 6726 10 -27 kg	1, 00727 a. eat.
			3, 3437 10 -27 kg	2.01355a. eat.
			5, 0075 10 -27 kg	3.01550 a. eat.
			5.0066 10 -27 kg	3.01493a. eat.
			6.6449 10 -27 kg	4.00151a. eat.
	Aluminum		44.7937 10 -27 kg	26.97441 a. eat.
	aluminum		49.7683 10 -27 kg	29.97008a. eat.

Let's find the energy that is released during the synthesis of one nucleus according to the formula:

The number of nuclei contained in the mass of 1 kg of helium can be found by the formula:

Then the total energy will be equal to: E=E 1 N; Plug in the data and do the calculations:

E \u003d 1.5 10 26 0.2817 10 -11 \u003d 4.2 10 14 J

Answer: 4.2 10 14 J

Literature 1. O.F. Kabardin, S.I. Kabardin "Typical test tasks", Publishing house "Exam" Moscow 2010.2. SOUTH. Pavlenko "The Beginnings of Physics", textbook, Exam Publishing House, Moscow 2005.3. G.Ya. Myakishev, B.B. Bukhovtsev "Physics, Grade 11", Moscow 2009 Publishing house "Enlightenment".

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What is the period of oscillation T of the pendulum if the experimenter took the division value of the stopwatch as the measurement error?

1) (4.12 ± 0.02) s 3) (4.12 ± 0.01) s

2) (4.12 ± 0.2) s 4) (4.12 ± 0.1) s

Answer:_________ (2 points)

24. In order to find the volume of the body as accurately as possible by immersing it in water, the students were asked to take measurements using two measuring cylinders with water (see Fig.). The students had to compare the measurement results, taking into account the absolute instrumental measurement errors and the absolute reading errors . Each of the errors taken into account was agreed to be considered equal to the division value of the measuring cylinder.

When answering the task question, the experimenters got four different results.

From the entries below, select the correct value of the measured body volume obtained with the smallest error

1) the first cylinder, (10 ± 10) cm 3

2) the first cylinder, (10 ± 5) cm 3

3) second cylinder, (10 ± 4) cm 3

4) second cylinder, (10 ± 2) cm 3

Answer:_________ (2 points)

25. In an elevator moving up with an acceleration of 2 m / s 2, there is a passenger weighing 50 kg. What is the modulus of gravity acting on the passenger?

Answer: __________N (4 points)

26. An ideal gas received an amount of heat of 300 J and did work of 100 J. How much did the internal energy of the gas increase in this case?

Answer: __________ J (4 points)

27. The oscillatory circuit consists of a capacitor with an electrical capacity of 50 microfarads and an inductance coil of 2 H. What is the cyclic frequency from free electromagnetic oscillations?

Answer: __________ rad/s (4 points)

28. In the experiment, it was found that at an air temperature in the bath of 60 ° C, condensation of water vapor from the air begins on the wall of a glass of water if the temperature of the glass is reduced to 29 ° C. Based on the results of these experiments, determine the relative humidity of the air. Use the table to solve the problem. With an increase in the air temperature in the room, the condensation of water vapor from the air begins at the same glass temperature of 29 ° C. Has the relative humidity changed?

Answer:__________% (4 points)

The solution of problems 29 - 32 is given in the solution form A-1. It must be complete; include laws and formulas, the application of which is necessary and sufficient to solve the problem, as well as mathematical transformations, calculations with a numerical answer and, if necessary, a figure explaining the solution.

29. In the attraction, a person weighing 100 kg makes a "dead loop" in a vertical plane. When the velocity vector was directed vertically downwards, the force of the normal pressure of a person on the seat was 2000 N. Find the speed of the trolley at this point with a circular path radius of 5 m.

Answer: ______________ (6 points)

30. The diagram (see figure) shows the changes in pressure and volume of an ideal monatomic gas. How much heat was received or given away by the gas during the transition from state 1 to state 3?

31. In a uniform magnetic field with an induction of 1.67 10 -5 T, a proton moves perpendicular to the induction vector B at a speed of 8 km / s. Determine the radius of the proton trajectory.

Answer: ______________ (6 points)

32. During the explosion of a thermonuclear bomb, energy of 8.3 10 16 J is released. This energy is obtained mainly due to the fission of uranium 238 nuclei. During the fission of one uranium 238 nucleus, 200 MeV is released, the mass of the nucleus is approximately 238 a.m.u. Calculate the mass of uranium nuclei that experienced fission during the explosion and the total mass defect.

Answer: ______________ (6 points)

Correction Form B