4.2.1. Prepare the scales and, with the permission of the laboratory assistant, weigh the body. Determine the instrumental error of the scales.

4.2.2. Record the measurement result in standard form: m=(m±Δm) [dimension].
5. CONCLUSION

Indicate whether the goal of the work has been achieved.

Record body weight measurements in two ways.

5.3. Compare results. Draw a conclusion
6. CONTROL QUESTIONS

6.1. What is inertial mass, gravitational mass, how are they defined? Formulate the principle of equivalence of inertial and gravitational mass.
6.2. What are direct measurements and indirect measurements? Give examples of direct and indirect measurements.
6.3. What is the absolute error of the measured quantity?
6.4. What is the relative error of the measured quantity?
6.5. What is the confidence interval of the measured quantity?
6.6. List the types of errors and give a brief description of them.
6.7. What is the accuracy class of the instrument? What is the price division of the device?
How is the instrumental error of the measurement result determined?
6.8. How the relative error and absolute error of indirect measurement are calculated.
6.9. How is the standard recording of the final measurement result made? What requirements must be met?

6.10. Measure the linear size of the body with a caliper. Record the measurement result in standard form.

6.11. Measure the linear size of the body with a micrometer. Record the result.

Laboratory work №2.

The study of the movement of the body in a circle

1. PURPOSE OF THE WORK. Determination of the centripetal acceleration of a ball during its uniform motion in a circle.

2. INSTRUMENTS AND ACCESSORIES. A tripod with a clutch and a foot, a ruler, a tape measure, a ball on a thread, a sheet of paper, a stopwatch.

BRIEF THEORY

The experiment is carried out with a conical pendulum (Fig. 1). Let a ball suspended on a thread describe a circle with a radius R. There are two forces acting on the ball: gravity and tension in the string. Their resultant creates a centripetal acceleration directed towards the center of the circle. The acceleration modulus can be determined using kinematics:

(1)

To determine the acceleration, it is necessary to measure the radius of the circle R and the period T circulation of the ball around the circle.
Centripetal acceleration can also be determined using Newton's 2nd law:

We choose the direction of the coordinate axes as shown in Fig.1. We project equation (2) onto the selected axes:

From equations (3) and (4) and from the similarity of triangles we get:

Fig.1. . (5)

Thus, using equations (1), (3) and (5), centripetal acceleration can be determined in three ways:

. (6)

Component module F x can be directly measured with a dynamometer. To do this, we pull the ball with a horizontally located dynamometer to a distance equal to the radius R circle (Fig. 1), and determine the dynamometer reading. In this case, the elastic force of the spring balances the horizontal component F x and equal in size.

In this paper, the task is to verify experimentally that the numerical values ​​of the centripetal acceleration obtained in three ways will be the same (the same within the absolute errors).

WORK TASK

1. Determine the mass m balls on the scales. Weighing result and instrumental error ∆ m write in table 1.

2. We draw a circle with a radius of about 20 cm on a piece of paper. We measure this radius, determine the instrumental error, and write the results in table 1.

3. Position the tripod with the pendulum so that the continuation of the thread passes through the center of the circle.

4. Take the thread with your fingers at the point of suspension and rotate the pendulum so that the ball describes the same circle as the circle drawn on paper.

5. Counting the time t, for which the ball makes a given number of revolutions (for example, N= 30) and estimate the error ∆ t measurements. The results are recorded in table 1.

6. Determine the height h conical pendulum and instrumental error ∆ h. Distance h measured vertically from the center of the ball to the point of suspension. The results are recorded in table 1.

7. We pull the ball with a horizontally located dynamometer to a distance equal to the radius R of the circle, and determine the dynamometer reading F= F x and instrumental error ∆ F. The results are recorded in table 1.

Table 1.

m

∆m

R

∆R

t

∆t

N

h

∆h

F

∆F

g

∆g

π

∆ π

G

G

mm

mm

with

with

mm

mm

H

H

m/s 2

m/s 2

8. Calculate the period T circulation of the ball around the circle and the error ∆ T:

.

9. Using formulas (6), we calculate the values ​​of centripetal acceleration in three ways and the absolute errors of indirect measurements of centripetal acceleration.

CONCLUSION

In the output, write in standard form the values ​​of centripetal acceleration obtained in three ways. Compare the obtained values ​​(see section "Introduction. Measurement errors"). Make a conclusion.

TEST QUESTIONS

6.1. What is a period T

6.2. How can you experimentally determine the period T the circle of the ball?

6.3. What is centripetal acceleration, how can it be expressed in terms of the period of revolution and in terms of the radius of the circle?

6.4. What is a conical pendulum. What forces act on the ball of a conical pendulum?

6.5. Write down Newton's 2nd law for a conical pendulum.

6.6. What are the three methods for determining centripetal acceleration offered in this lab?

6.7. What measuring devices are used to determine the values ​​of the physical quantities given in Table 1?

6.8. Which of the three methods for determining centripetal acceleration gives the most accurate value of the measured quantity?

Lab #3

Similar information.

Laboratory work No. 4 in physics Grade 9 (answers) - Studying the movement of a body in a circle

3. Calculate and enter in the table the average value of the time interval , for which the ball makes N = 10 revolutions.

4. Calculate and enter in the table the average value of the rotation period ball.

5. Using formula (4), determine and enter in the table the average value of the acceleration module.

6. Using formulas (1) and (2), determine and enter in the table the average value of the angular and linear velocity modules.

Experience	N	t	T	a	ω	v
1	10	12.13	-	-	-	-
2	10	12.2	-	-	-	-
3	10	11.8	-	-	-	-
4	10	11.41	-	-	-	-
5	10	11.72	-	-	-	-
Wed	10	11.85	1.18	4.25	0.63	0.09

7. Calculate the maximum value of the absolute random error in measuring the time interval t.

8. Determine the absolute systematic error of the time interval t.

9. Calculate the absolute error of direct measurement of the time interval t.

10. Calculate the relative error of the direct measurement of the time interval.

11. Record the result of a direct measurement of the time interval in interval form.

Answer security questions

1. How will the linear speed of the ball change with its uniform rotational motion relative to the center of the circle?

Linear speed is characterized by direction and magnitude (modulus). The modulus is a constant value, and the direction during such a movement can change.

2. How to prove the relation v = ωR?

Since v = 1/T, the relationship of the cyclic frequency with the period and frequency is 2π = VT, whence V = 2πR. Relationship between linear velocity and angular velocity 2πR = VT, hence V = 2πr/T. (R is the radius of the inscribed, r is the radius of the inscribed)

3. How does the period of rotation T of the ball depend on the module of its linear velocity?

The higher the rate, the shorter the period.

Conclusions: I learned to determine the period of rotation, modules, centripetal acceleration, angular and linear speeds with uniform rotation of the body and calculate the absolute and relative errors of direct measurements of the time interval of the body's movement.

Supertask

Determine the acceleration of a material point during its uniform rotation, if in Δt = 1 s it passed 1/6 of the circumference, having a linear velocity modulus v = 10 m/s.

Circumference:

S = 10 ⋅ 1 = 10 m
l \u003d 10⋅ 6 \u003d 60 m

Circle radius:

r = l/2π
r = 6/2 ⋅ 3 = 10 m

Acceleration:

a = v 2 /r
a \u003d 100 2 / 10 \u003d 10 m / s 2.

.

IPreparatory stage

The figure schematically shows the swing, known as "giant steps". Find the centripetal force, radius, acceleration and speed of a person swinging around a pole. The length of the rope is 5 m, the mass of a person is 70 kg. The pole and the rope form an angle of 300 during circulation. Determine the period if the rotation frequency of the swing is 15 min-1.

Hint: A body rotating in a circle is affected by gravity and the elastic force of the rope. Their resultant imparts centripetal acceleration to the body.

Enter the results of the calculations in the table:

Turnaround time, s

Speed

Period of circulation, s

Radius of circulation, m

Body weight, kg

centripetal force, N

circulation speed, m/s

centripetal acceleration, m/s2

II. main stage

Objective:

Devices and materials:

1. Before the experiment, a load, previously weighed on a balance, is suspended on a thread to the leg of the tripod.

2. Under the hanging load, place a sheet of paper with a circle drawn on it with a radius of 15-20 cm. Place the center of the circle on a plumb line passing through the point of suspension of the pendulum.

3. At the point of suspension, the thread is taken with two fingers and the pendulum is carefully brought into rotational motion, so that the radius of rotation of the pendulum coincides with the radius of the drawn circle.

4. Bring the pendulum into rotation and counting the number of revolutions, measure the time during which these revolutions occurred.

5. Record the results of measurements and calculations in the table.

6. The resultant force of gravity and the force of elasticity, found during the experiment, is calculated from the parameters of the circular movement of the load.

On the other hand, the centripetal force can be determined from the proportion

Here, the mass and radius are already known from previous measurements, and in order to determine the centrifugal force in the second way, it is necessary to measure the height of the suspension point above the rotating ball. To do this, pull the ball to a distance equal to the radius of rotation and measure the vertical distance from the ball to the suspension point.

7. Compare the results obtained in two different ways and draw a conclusion.

IIIcontrol stage

In the absence of scales at home, the purpose of work and equipment can be changed.

Objective: measurement of linear velocity and centripetal acceleration in uniform circular motion

Devices and materials:

1. Take a needle with a double thread 20-30 cm long. Insert the tip of the needle into an eraser, a small onion or a plasticine ball. You will receive a pendulum.

2. Raise your pendulum by the free end of the thread above a sheet of paper lying on the table, and bring it into uniform rotation around the circle shown on the sheet of paper. Measure the radius of the circle along which the pendulum moves.

3. Achieve a stable rotation of the ball along a given trajectory and use the clock with a second hand to fix the time for 30 revolutions of the pendulum. Using known formulas, calculate the modules of linear velocity and centripetal acceleration.

4. Make a table to record the results and fill it out.

References:

1. Frontal laboratory classes in physics in high school. Manual for teachers edited. Ed. 2nd. - M., "Enlightenment", 1974

2. Shilov work at school and at home: mechanics.-M .: "Enlightenment", 2007

Date__________ FI_____________________________________ Grade 10_____

Laboratory work No. 1 on the topic:

"STUDYING THE MOVEMENT OF A BODY IN A CIRCLE UNDER THE ACTION OF FORCES OF ELASTICITY AND GRAVITY".

Objective: determination of the centripetal acceleration of the ball during its uniform motion in a circle.

Equipment: tripod with clutch and foot, measuring tape, compasses, dynamometer

laboratory, scales with weights, weight on threads, sheet of paper, ruler, cork.

Theoretical part of the work.

Experiments are carried out with a conical pendulum. A small ball moves along a circle of radius R. In this case, the thread AB, to which the ball is attached, describes the surface of a right circular cone. There are two forces acting on the ball: the force of gravity
and thread tension (Fig. a). They create centripetal acceleration directed along the radius towards the center of the circle. The acceleration modulus can be determined kinematically. It is equal to:

.

To determine the acceleration, it is necessary to measure the radius of the circle and the period of revolution of the ball around the circle.

Centripetal (normal) acceleration can also be determined using the laws of dynamics.

According to Newton's second law
. Let's decompose the force into components and , directed along the radius to the center of the circle and vertically upwards.

Then Newton's second law is written as follows:

.

We choose the direction of the coordinate axes as shown in Figure b. In projections onto the O 1 y axis, the equation of motion of the ball will take the form: 0 = F 2 - mg. Hence F 2 = mg: component balances the force of gravity
acting on the ball.

Let's write Newton's second law in projections onto the O 1 x axis: ma n = F 1 . From here
.

The module component F 1 can be determined in various ways. First, this can be done from the similarity of triangles OAB and FBF 1:

.

From here
and
.

Secondly, the modulus of the component F 1 can be directly measured with a dynamometer. To do this, we pull the ball with a horizontally located dynamometer to a distance equal to the radius R of the circle (Fig. c), and determine the dynamometer reading. In this case, the elastic force of the spring balances the component .

Let's compare all three expressions for a n:

,
,
and make sure they are close to each other.

Working process.

1. Determine the mass of the ball on the balance to the nearest 1 g.

2. Attach the ball suspended on a thread to the leg of the tripod using a piece of cork.

3 . Draw a circle with a radius of 20 cm on a piece of paper. (R= 20 cm = _______ m).

4. We position the tripod with the pendulum so that the extension of the cord passes through the center of the circle.

5 . Taking the thread with your fingers at the point of suspension, set the pendulum in rotational motion

over a sheet of paper so that the ball describes the same circle as the one drawn on the paper.

6. We count the time during which the pendulum makes 50 full revolutions (N = 50).

7. Calculate the period of revolution of the pendulum using the formula: T = t / N.

8 . Calculate the value of centripetal acceleration using formula (1):

=

9 . Determine the height of the conical pendulum (h). To do this, measure the vertical distance from the center of the ball to the suspension point.

10 . Calculate the value of centripetal acceleration using formula (2):

=

11. Pull the ball horizontally with a dynamometer to a distance equal to the radius of the circle, and measure the modulus of the component .

Then we calculate the acceleration using formula (3): =

12. The results of measurements and calculations are entered in the table.

Circle radius R , m	Speed N	t , with	Period of circulation T = t / N	pendulum height h , m	Ball mass m , kg	Central acceleration m/s 2	Central acceleration m/s 2	Central acceleration m/s 2

13 . Compare the obtained three values ​​of the centripetal acceleration module.

__________________________________________________________________________ CONCLUSION:

______________________________________________________________________________________________________________________________________________________________________________________________________________________________

Additionally:

Find the relative and absolute error of indirect measurement a u (1) and (3):

Formula 1). _______ ; Δa c \u003d a c \u003d ________;

Formula (3). _________; Δa c \u003d a c \u003d _______.

3. Calculate and enter in the table the average value of the time interval<t> for which the ball makes N= 10 turns.

4. Calculate and enter in the table the average value of the rotation period<T> ball.

5. Using formula (4), determine and enter in the table the average value of the acceleration module.

6. Using formulas (1) and (2), determine and enter in the table the average value of the angular and linear velocity modules.

Experience	N	t	T	a	ω	v
1	10	12.13	—	—	—	—
2	10	12.2	—	—	—	—
3	10	11.8	—	—	—	—
4	10	11.41	—	—	—	—
5	10	11.72	—	—	—	—
Wed	10	11.85	1.18	4.25	0.63	0.09

7. Calculate the maximum value of the absolute random error in the measurement of the time interval t.

8. Determine the absolute systematic error of the time interval t .

9. Calculate the absolute error of the direct measurement of the time interval t .

10. Calculate the relative error of the direct measurement of the time interval.

11. Record the result of a direct measurement of the time interval in interval form.

Answer security questions

1. How will the linear speed of the ball change with its uniform rotational motion relative to the center of the circle?

Linear speed is characterized by direction and magnitude (modulus). The modulus is a constant value, and the direction can change during such a movement.

2. How to prove the ratio v = ωR?

Since v = 1/T, the relation of the cyclic frequency to the period and frequency is 2π = VT, whence V = 2πR. Relationship between linear velocity and angular velocity 2πR = VT, hence V = 2πr/T. (R is the radius of the circumscribed, r is the radius of the inscribed)

3. How the rotation period depends T ball from the module of its linear velocity?

The higher the rate, the shorter the period.

Findings: learned to determine the period of rotation, modules, centripetal acceleration, angular and linear velocities with uniform rotation of the body and calculate the absolute and relative errors of direct measurements of the time interval of the body's movement.

Supertask

Determine the acceleration of a material point during its uniform rotation, if for Δ t\u003d 1 s it traveled 1/6 of the circumference, having the linear velocity modulus v= 10 m/s.

Circumference:

S = 10 ⋅ 1 = 10 m
l \u003d 10⋅ 6 \u003d 60 m

Circle radius:

r = l/2π
r = 6/2 ⋅ 3 = 10 m

Acceleration:

a = v 2/r
a = 100 2/10 = 10 m/s2.