Force can act only on a material body, which necessarily has mass. Using Newton's second law, you can determine the mass of the body on which the force has acted. Depending on the nature of the force, additional quantities may be needed to define mass in terms of force.
You will need
- - accelerometer;
- - roulette;
- - stopwatch;
- - calculator.
Instruction
To calculate the mass of a body subjected to a known force, use the ratio derived from Newton's second law. To do this, use an accelerometer to measure the acceleration that the body received as a result of the force. If this device is not available, measure the speed at the beginning and end of the observation time of the body and divide the change in speed by the time. This will be the average acceleration of the body over the measured period of time. Calculate the mass by dividing the value of the force acting on the body F, measured in m / s? acceleration a, m=F/a. If the value of the force is taken in Newtons, then the mass will be obtained in kilograms.
Calculate the mass of the body on which the force of gravity acts. To do this, hang it on a dynamometer and on the scale determine the force that acts on the body. This will be the force of gravity. In order to determine the mass of the body, divide the value of this force Ft by the free fall acceleration g? 9.81 m / s?, m \u003d F / g. For convenience, in the calculations, you can take the value g? 10 m / s? in the event that high accuracy in determining the mass value in kilograms is not required.
When a body moves along a circular path at a constant speed, a force also acts on it. If its value is known, find the mass of a body moving along a circular path. To do this, measure or calculate the speed of the body. Measure with a speedometer if possible. To calculate the speed, measure the radius of the body trajectory with a tape measure or ruler R and the time for a complete revolution T with a stopwatch, this is called the period of rotation. The speed will be equal to the product of the radius and the number 6.28, divided by the period. Find the mass by multiplying the force F by the radius of the body's trajectory and dividing the result by the square of its speed m=F R/v?. To get the result in kilograms, measure the speed in meters per second, the radius in meters, and the force in Newtons.
I did not understand the lesson in physics and I do not know how to determine the force of gravity!
Answer
Gravity is the property of bodies with mass to attract each other. Bodies that have mass always attract each other. The attraction of bodies with very large masses on an astronomical scale creates significant forces due to which the world is as we know it.
The force of gravity is the cause of the earth's gravity, as a result of which objects fall on it. Due to the force of gravity, the Moon revolves around the Earth, the Earth and other planets around the Sun, and the Solar System around the center of the Galaxy.
In physics, gravity is the force with which a body acts on a support or vertical suspension. This force is always directed vertically downwards.
F is the force with which the body acts. It is measured in newtons (N).
m is the mass (weight) of the body. Measured in kilograms (kg)
g is the free fall acceleration. It is measured in newtons divided by the kilogram (N/kg). Its value is constant and on average over the earth's surface is 9.8 N/kg.
How to determine the force of attraction?
Example:
Let the mass of the suitcase be 15 kg, then to find the force of attraction of the suitcase to the Earth, we use the formula:
F \u003d m * g \u003d 15 * 9.8 \u003d 147 N.
That is, the force of attraction of the suitcase is 147 newtons.
The value of g for the planet Earth is not the same - at the equator it is 9.83 N/kg, and at the poles 9.78 N/kg. Therefore, they take the average value that we used for the calculation. Accurate values for different regions of the planet are used in the aerospace industry, and they are also paid attention to in sports, when athletes train for competitions in other countries.
Historical note: for the first time he calculated g and derived the formula for gravity, or rather the formula for the force with which a body acts on other bodies, in 1687, the famous English physicist Isaac Newton. It is in his honor that the unit of measurement of force is named. There is a legend that Newton began to investigate the issue of gravity after an apple fell on his head.
How find the speed of a body, knowing its mass and the force applied to it?
There is a projectile of 5 grams, a force of 1.5N was applied to it.
Friction force - Physics in experiments and experiments
Is there any way to find out its speed?
If so, what other characteristics should be known?
Let's imagine that we have these characteristics. What formula will then be used to calculate the speed of this body?
No additional features. Force is a precondition for acceleration according to Newton's second law a=F/m. But the speed at each moment of time is found by the formula v=v0at. Therefore, in order to find out the speed, it is also necessary to know its initial value and how much time has passed from now on.
But if we are talking specifically about the projectile, then everything becomes much more complicated. The force is applied to the projectile only until the moment the projectile leaves the barrel and, moreover, is not constant. The force itself changes in proportion to the pressure of the powder gases. The pressure curve is shown in the figure.
The calculation of speed and pressure is already carried out according to ballistic formulas, for example, as follows:
where l is the path in the barrel, L is the length of the rifled part, a,b,φ are powder constants, S is the cross-sectional area of the barrel.
But even in a slingshot, the resulting force is not constant, but backwards proportional to the tension of the rubber, and the initial speed will depend on this variable force, mass and time of the shot. Therefore, according to those data (only force and mass), you can actually calculate nothing.
In this case, you need to apply 2 Newton's law, but not in the usual form for us, but in a differential one:
F=(p2-p1)/t, where F is the force applied to the body, p1 is the momentum of the body before applying the force, p2 is the momentum of the body after application of force, t - time of force application.
In other words, the resulting value of the force applied to the body is the change in the momentum of this body per unit of time. It was in this form that Newton derived his own law.
Let's apply this formula.
As I understand it, the original projectile speed is 0, as follows the 2nd Newton's law takes the form:
Having painted the momentum and expressing the speed, we have:
It can be seen from the acquired formula that in order to find the speed, we should know the time. Indeed, the more time the force is applied to the body, the more it will accelerate the body (or slow it down if the direction of the force and the direction of the velocity are opposite).
Imagine that t=1 s.
Thus, to find the speed of the body, in this case, we must know the force acting on the body, the mass of the body, and the time the force acted on the body (assuming that the body was at rest).
Let someone correct me if I'm wrong, but in my opinion here is Newton's 2nd law. In general terms, this is personal from the force divided by the mass!
If a force of 1.5 N is applied (and not removed) to a body with a mass of 5 g, then, according to Newton's second law, it will give it an acceleration a = F / m = 1.5 / 0.005 = 300 m / s ^ 2. Under the action of this acceleration, the body will begin to increase its speed according to the law v=at, where t is the time of the force. So, knowing the formula, you can calculate the speed of the body in any moment of time.
In a second - 1.5 / 0.005 \u003d 300 m / s. After 2 seconds - 600 m / s. After 3 seconds - 900 m / s. After 4 seconds - 1.2 km / s. After 5 seconds - 1.5 km / s. After 10 seconds - 3 km / s. After 20 seconds - 6 km / s. And in half a minute, the speed will reach 8 km / s, and if the projectile does not stick into the Earth by that time, it will begin to move away from the Earth's surface.
If we consider this issue from the point of view of school knowledge, then F \u003d ma, F - force, m - mass, a - acceleration. To find the speed at any moment of time, it is enough to multiply the acceleration by the time. If we take into account that there is a friction force, then that the force was not applied uniformly and not constantly, then additional data are needed.
The speed can be determined by the formula: v = Ft/m.
That is, in order to successfully solve the problem, we lack one more physical quantity, namely, time.
Abstracts
How to find mass, knowing strength in 2017 how to find out. How to find strength friction slip f friction formula. How to determine coefficient of friction slip? Here, the elastic force of the dynamometer spring balances force friction How knowing mass. How to find the coefficient of friction? Friction force formula. It always exists, since absolutely smooth bodies do not exist. Find friction force. Please tell me how to find. which will pass the body, knowing the power friction, mass and speed of the body??? We find force friction. Friction force formula. Before finding the force of friction, the formula of which takes on a different form (f=? How to find acceleration - wikiHow. How to find acceleration. to find acceleration, divide the force by the mass of the accelerating. How to calculate the force. Find the mass, knowing strength and acceleration. If you know the force and acceleration of an object, How. how find- Coefficient of friction knowing mass and force. School knowledge.
Acceleration characterizes the rate of change in the speed of a moving body. If the speed of a body remains constant, then it does not accelerate.
Acceleration takes place only when the speed of the body changes. If the speed of a body increases or decreases by some constant value, then such a body moves with constant acceleration. Acceleration is measured in meters per second per second (m/s2) and is calculated from two velocities and time, or from a force applied to a body.
Steps
- 1 a = ∆v / ∆t
- 2 Definition of variables. You can calculate Δv and Δt in the following way: Δv \u003d vk - vn and Δt \u003d tk - tn, where vk- final speed vн- starting speed, tk- end time tn- start time.
- 3
- Write the formula: a \u003d Δv / Δt \u003d (vk - vn) / (tk - tn)
- Write variables: vk= 46.1 m/s, vн= 18.5 m/s, tk= 2.47 s, tn= 0 s.
- Calculation: a
- Write the formula: a \u003d Δv / Δt \u003d (vk - vn) / (tk - tn)
- Write variables: vk= 0 m/s, vн= 22.4 m/s, tk= 2.55 s, tn= 0 s.
- Calculation: a
- 1 Newton's second law.
- Fres = m x a, where Fres m- body mass, a is the acceleration of the body.
- 2 Find the mass of the body.
- Remember that 1 N = 1 kg∙m/s2.
- a = F/m = 10/2 = 5 m/s2
3 Testing your knowledge
- 1 direction of acceleration.
- 2 Direction of force.
- 3 resultant force.
- Solution: The condition of this problem is designed to confuse you. In fact, everything is very simple. Draw a diagram of the direction of forces, so you will see that a force of 150 N is directed to the right, a force of 200 N is also directed to the right, but a force of 10 N is directed to the left. Thus, the resulting force is: 150 + 200 - 10 = 340 N. The acceleration is: a = F/m = 340/400 = 0.85 m/s2.
Determining the force or moment of force, if the mass or moment of inertia of the body is known, allows you to find out only the acceleration, that is, how quickly the speed will change
Shoulder of Strength- a perpendicular dropped from the axis of rotation to the line of action of the force.
Bone links in the human body are levers. In this case, the result of the action of a muscle is determined not so much by the force developed by it, but by the moment of force. A feature of the structure of the human musculoskeletal system is the small values of the shoulders of the traction forces of the muscles. At the same time, an external force, such as gravity, has a large shoulder (Fig. 3.3). Therefore, in order to counteract large external moments of forces, the muscles must develop a large traction force.
Rice. 3.3. Features of the work of human skeletal muscles
The moment of force is considered positive if the force causes the body to rotate counterclockwise, and negative when the body rotates clockwise. On fig. 3.3. the gravity of the dumbbell creates a negative moment of force, as it tends to rotate the forearm in the elbow joint clockwise. The traction force of the flexor muscles of the forearm creates a positive moment, as it tends to rotate the forearm in the elbow joint counterclockwise.
momentum impulse(Sm) - a measure of the impact of the moment of force relative to a given axis over a period of time.
momentum (To) & vector quantity, a measure of the rotational motion of a body, characterizing its ability to be transmitted to another body in the form of mechanical motion. The momentum is determined by the formula: K=J .
The momentum during rotational motion is analogous to the momentum of the body (momentum) during translational motion.
Example. When performing a jump into the water after performing a repulsion from the bridge, the kinetic moment of the human body ( To) remains unchanged. Therefore, if the moment of inertia (J) is reduced, that is, to group, the angular velocity increases. Before entering the water, the athlete increases the moment of inertia (straightens), thereby reducing the angular velocity of rotation.
How to find acceleration through force and mass?
How much the speed has changed can be found by determining the momentum of the force. Impulse of force - a measure of the impact of force on the body for a given period of time (in translational motion): S = F*Dt = m*Dv. In the case of the simultaneous action of several forces, the sum of their momenta is equal to the momentum of their resultant for the same time. It is the impulse of the force that determines the change in speed. In rotational motion, the impulse of the force corresponds to the impulse of the moment of force - a measure of the impact of force on the body relative to a given axis for a given period of time: Sz = Mz * Dt.
Due to the impulse of the force and the momentum of the moment of force, changes in motion occur, depending on the inertial characteristics of the body and manifested in changes in speed (momentum and moment of momentum - kinetic moment).
The amount of motion is a measure of the translational motion of a body, characterizing the ability of this motion to be transmitted to another body: K = m * v. The change in momentum is equal to the momentum of the force: DK = F*Dt = m*Dv = S.
Momentum is a measure of the rotational motion of a body, characterizing the ability of this motion to be transmitted to another body: Kya = I*w = m*v*r. If the body is connected to an axis of rotation that does not pass through its CM, then the total angular momentum is composed of the angular momentum of the body about the axis passing through its CM parallel to the external axis (I0 * w) and the angular momentum of some point that has the mass of the body and is spaced from the axis rotation at the same distance as the CM: L = I0*w + m*r2*w.
There is a quantitative relationship between the moment of momentum (kinetic moment) and the moment of impulse of the force: DL = Mz*Dt = I*Dw = Sz.
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Acceleration characterizes the rate of change in the speed of a moving body. If the speed of a body remains constant, then it does not accelerate. Acceleration takes place only when the speed of the body changes. If the speed of a body increases or decreases by some constant value, then such a body moves with constant acceleration. Acceleration is measured in meters per second per second (m/s2) and is calculated from two velocities and time, or from a force applied to a body.
Steps
1 Calculation of the average acceleration over two speeds
- 1 Formula for calculating the average acceleration. The average acceleration of a body is calculated from its initial and final velocities (speed is the speed of movement in a certain direction) and the time it takes the body to reach the final speed. Formula for calculating acceleration: a = ∆v / ∆t, where a is the acceleration, Δv is the change in speed, Δt is the time required to reach the final speed.
- The units of acceleration are meters per second per second, that is, m/s2.
- Acceleration is a vector quantity, that is, it is given both by value and direction. Value is a numerical characteristic of acceleration, and direction is the direction of movement of the body. If the body slows down, then the acceleration will be negative.
- 2 Definition of variables. You can calculate Δv and Δt in the following way: Δv \u003d vk - vn and Δt \u003d tk - tn, where vk- final speed vн- starting speed, tk- end time tn- start time.
- Since acceleration has a direction, always subtract the initial velocity from the final velocity; otherwise, the direction of the calculated acceleration will be wrong.
- If the initial time is not given in the problem, then it is assumed that tn = 0.
- 3 Find the acceleration using the formula. First, write the formula and the variables given to you. Formula: a \u003d Δv / Δt \u003d (vk - vn) / (tk - tn). Subtract the initial speed from the final speed, and then divide the result by the time span (change in time). You will get the average acceleration for a given period of time.
- If the final speed is less than the initial one, then the acceleration has a negative value, that is, the body slows down.
- Example 1: A car accelerates from 18.5 m/s to 46.1 m/s in 2.47 s. Find the average acceleration.
- Write the formula: a \u003d Δv / Δt \u003d (vk - vn) / (tk - tn)
- Write variables: vk= 46.1 m/s, vн= 18.5 m/s, tk= 2.47 s, tn= 0 s.
- Calculation: a\u003d (46.1 - 18.5) / 2.47 \u003d 11.17 m / s2.
- Example 2: A motorcycle starts braking at 22.4 m/s and stops after 2.55 seconds. Find the average acceleration.
- Write the formula: a \u003d Δv / Δt \u003d (vk - vn) / (tk - tn)
- Write variables: vk= 0 m/s, vн= 22.4 m/s, tk= 2.55 s, tn= 0 s.
- Calculation: a\u003d (0 - 22.4) / 2.55 \u003d -8.78 m / s2.
2 Calculation of acceleration by force
- 1 Newton's second law. According to Newton's second law, a body will accelerate if the forces acting on it do not balance each other. Such acceleration depends on the resultant force acting on the body. Using Newton's second law, you can find the acceleration of a body if you know its mass and the force acting on that body.
- Newton's second law is described by the formula: Fres = m x a, where Fres is the resultant force acting on the body, m- body mass, a is the acceleration of the body.
- When working with this formula, use the units of the metric system, in which mass is measured in kilograms (kg), force in newtons (N), and acceleration in meters per second per second (m/s2).
- 2 Find the mass of the body. To do this, put the body on the scales and find its mass in grams. If you are looking at a very large body, look up its mass in reference books or on the Internet. The mass of large bodies is measured in kilograms.
- To calculate the acceleration using the above formula, you must convert grams to kilograms. Divide the mass in grams by 1000 to get the mass in kilograms.
- 3 Find the resultant force acting on the body. The resulting force is not balanced by other forces. If two oppositely directed forces act on a body, and one of them is greater than the other, then the direction of the resulting force coincides with the direction of the greater force. Acceleration occurs when a force acts on a body, which is not balanced by other forces and which leads to a change in the speed of the body in the direction of this force.
- For example, you and your brother are pulling a rope. You are pulling the rope with a force of 5 N and your brother is pulling the rope (in the opposite direction) with a force of 7 N. The net force is 2 N and is directed towards your brother.
- Remember that 1 N = 1 kg∙m/s2.
- 4 Transform the formula F = ma to calculate the acceleration. To do this, divide both sides of this formula by m (mass) and get: a = F / m. Thus, to find the acceleration, divide the force by the mass of the accelerating body.
- The force is directly proportional to the acceleration, that is, the greater the force acting on the body, the faster it accelerates.
- Mass is inversely proportional to acceleration, that is, the greater the mass of the body, the slower it accelerates.
- 5 Calculate the acceleration using the resulting formula. Acceleration is equal to the quotient of the resultant force acting on the body divided by its mass. Substitute the values given to you into this formula to calculate the body's acceleration.
- For example: a force equal to 10 N acts on a body of mass 2 kg. Find the acceleration of the body.
- a = F/m = 10/2 = 5 m/s2
3 Testing your knowledge
- 1 direction of acceleration. The scientific concept of acceleration does not always coincide with the use of this quantity in everyday life. Remember that acceleration has a direction; acceleration has a positive value if it is directed upwards or to the right; acceleration has a negative value if it is directed downwards or to the left. Check the correctness of your solution based on the following table:
- 2 Direction of force. Remember that acceleration is always co-directional with the force acting on the body. In some tasks, data is given whose purpose is to mislead you.
- Example: A toy boat with a mass of 10 kg is moving north with an acceleration of 2 m/s2. A wind blowing in a westerly direction acts on a boat with a force of 100 N. Find the acceleration of the boat in a northerly direction.
- Solution: Since the force is perpendicular to the direction of motion, it does not affect the motion in that direction. Therefore, the acceleration of the boat in the north direction will not change and will be equal to 2 m/s2.
- 3 resultant force. If several forces act on the body at once, find the resulting force, and then proceed to calculate the acceleration. Consider the following problem (in two dimensions):
- Vladimir pulls (on the right) a 400 kg container with a force of 150 N. Dmitry pushes (on the left) a container with a force of 200 N. The wind blows from right to left and acts on the container with a force of 10 N. Find the acceleration of the container.
- Solution: The condition of this problem is designed to confuse you. In fact, everything is very simple.
Newton's second law
Draw a diagram of the direction of forces, so you will see that a force of 150 N is directed to the right, a force of 200 N is also directed to the right, but a force of 10 N is directed to the left. Thus, the resulting force is: 150 + 200 - 10 = 340 N. The acceleration is: a = F/m = 340/400 = 0.85 m/s2.
Sent by: Veselova Kristina. 2017-11-06 17:28:19
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Lesson 5. DEPENDENCE OF MASS ON SPEED. RELATIVISTIC DYNAMICS
The laws of Newton's mechanics do not agree with the new spatio-temporal concepts at high speeds. Only at low speeds, when the classical concepts of space and time are valid, Newton's second law
does not change its shape when moving from one inertial frame of reference to another (the principle of relativity is satisfied).
But at high speeds, this law in its usual (classical) form is unfair.
According to Newton's second law (2.4), a constant force acting on a body for a long time can impart an arbitrarily high speed to the body. But in reality, the speed of light in a vacuum is the limit, and under no circumstances can a body move at a speed exceeding the speed of light in a vacuum. A very small change in the equation of motion of bodies is required for this equation to be true at high speeds of motion. First, let's move on to the form of writing the second law of dynamics, which was used by Newton himself:
where is the momentum of the body. In this equation, body mass was considered independent of speed.
It is striking that equation (2.5) does not change its form even at high speeds.
The changes concern only the mass. As the speed of a body increases, its mass does not remain constant, but increases.
The dependence of mass on velocity can be found based on the assumption that the law of conservation of momentum is also valid under new ideas about space and time. The calculations are too complicated. We present only the final result.
If through m0 denote the mass of the body at rest, then the mass m the same body, but moving at a speed , is determined by the formula
Figure 43 shows the dependence of body mass on its speed. It can be seen from the figure that the increase in mass is the greater, the closer the speed of the body to the speed of light With.
 |
At speeds of motion much less than the speed of light, the expression differs very little from unity. So, at a speed more modern than a space rocket u" 10 km/s we get =0,99999999944 .
It is not surprising, therefore, that it is impossible to notice an increase in mass with an increase in speed at such relatively low speeds of movement. But elementary particles in modern particle accelerators reach enormous speeds. If the speed of a particle is only 90 km/s less than the speed of light, then its mass increases by 40 times.
Calculation of force F
Powerful electron accelerators are capable of accelerating these particles to speeds that are only 35-50 m/s less than the speed of light. In this case, the mass of the electron increases by about 2000 times. In order for such an electron to be kept in a circular orbit, a force must act on it from the side of the magnetic field, 2000 times greater than one would expect, not taking into account the dependence of mass on speed. It is no longer possible to use Newtonian mechanics to calculate the trajectories of fast particles.
Taking into account relation (2.6), the momentum of the body is equal to:
The basic law of relativistic dynamics is written in the same form:
However, the momentum of the body, here is determined by the formula (2.7), and not just the product.
Thus, mass, thought to be constant since Newton's time, actually depends on velocity.
As the speed of movement increases, the mass of the body, which determines its inertial properties, increases. At u®c body mass in accordance with equation (2.6) increases indefinitely ( m®¥); therefore, the acceleration tends to zero and the speed practically ceases to increase, no matter how long the force acts.
The need to use the relativistic equation of motion in the calculation of charged particle accelerators means that the theory of relativity has become an engineering science in our time.
The laws of Newton's mechanics can be considered as a special case of relativistic mechanics, which is valid at the speeds of motion of bodies much less than the speed of light.
The relativistic equation of motion, which takes into account the dependence of mass on velocity, is used in the design of elementary particle accelerators and other relativistic devices.
? 1 . Write down the formula for the dependence of body mass on the speed of its movement. 2 . Under what condition can the mass of a body be considered independent of speed?
formulas in mathematics, linear algebra and geometry
§ 100. Expression of kinetic energy in terms of mass and speed of a body
In §§ 97 and 98 we saw that it is possible to create a store of potential energy by causing some force to do work by lifting a load or compressing a spring. In the same way, it is possible to create a supply of kinetic energy as a result of the work of any force. Indeed, if a body receives acceleration under the action of an external force and moves, then this force does work, and the body acquires speed, i.e., acquires kinetic energy. For example, the pressure force of powder gases in the barrel of a gun, pushing a bullet, does work, due to which a reserve of kinetic energy of the bullet is created. Conversely, if due to the movement of the bullet work is done (for example, the bullet rises up or, hitting an obstacle, produces destruction), then the kinetic energy of the bullet decreases.
We can trace the transition of work into kinetic energy using an example when only one force acts on the body (in the case of many forces, this is the resultant of all forces acting on the body). Suppose that a constant force began to act on a body of mass , which was at rest; under the action of a force, the body will move uniformly with acceleration . Having traveled a distance in the direction of the force, the body will acquire a speed related to the distance traveled by the formula (§ 22). From here we find the work of the force:
.
In the same way, if a force directed against its movement begins to act on a body moving at a speed, then it will slow down its movement and stop, having done work against the acting force, also equal to . This means that the kinetic energy of a moving body is equal to half the product of its mass and the square of its speed:
Since the change in kinetic energy, as well as the change in potential energy, is equal to the work (positive or negative) produced by this change, the kinetic energy is also measured in units of work, i.e., in joules.
100.1. A body of mass moves with speed by inertia. A force begins to act on the body along the direction of motion of the body, as a result of which, after a while, the speed of the body becomes equal to . Show that the increase in the kinetic energy of the body is equal to the work produced by the force, for the case when the speed: a) increases; b) is decreasing; c) changes sign.
100.2. What is a lot of work spent on: to inform a train at rest of a speed of 5 m/s or to accelerate it from a speed of 5 m/s to a speed of 10 m/s?
How to find the mass of a car in physics
How to find the mass, knowing the speed
You will need
- - a pen;
- - note paper.
Instruction
The simplest case is the movement of one body with a given uniform speed. The distance traveled by the body is known. Find the travel time: t = S/v, hour, where S is the distance, v is the average speed of the body.
The second example is for the oncoming movement of bodies. A car is moving from point A to point B at a speed of 50 km/h. A moped simultaneously left point B to meet him at a speed of 30 km/h. The distance between points A and B is 100 km. It is required to find the time after which they will meet.
Designate the meeting point with the letter K. Let the distance AK that the car traveled be x km. Then the path of the motorcyclist will be 100 km. It follows from the condition of the problem that the travel time for a car and a moped is the same. Write the equation: x / v \u003d (S-x) / v ', where v, v ' are the speeds of the car and the moped. Substituting the data, solve the equation: x = 62.5 km. Now find the time: t = 62.5/50 = 1.25 hours or 1 hour 15 minutes. The third example - the same conditions are given, but the car left 20 minutes later than the moped. Determine how long the car will travel before meeting the moped. Write an equation similar to the previous one. But in this case, the moped's travel time will be 20 minutes longer than that of the car. To equalize parts, subtract one third of an hour from the right side of the expression: x/v = (S-x)/v'-1/3. Find x - 56.25. Calculate the time: t = 56.25/50 = 1.125 hours or 1 hour 7 minutes 30 seconds.
The fourth example is the problem of the movement of bodies in one direction. A car and a moped move from point A at the same speed. It is known that the car left half an hour later. How long will it take him to overtake the moped?
In this case, the distance traveled by vehicles will be the same. Let the travel time of the car be x hours, then the travel time of the moped will be x + 0.5 hours. You have an equation: vx = v'(x+0.5). Solve the equation by plugging in the speed and find x - 0.75 hours or 45 minutes.
The fifth example - a car and a moped with the same speeds are moving in the same direction, but the moped left point B, located at a distance of 10 km from point A, half an hour earlier. Calculate how long after the start the car will overtake the moped.
The distance traveled by the car is 10 km more. Add this difference to the rider's path and equalize the parts of the expression: vx = v'(x+0.5)-10. Substituting the speed values and solving it, you will get the answer: t = 1.25 hours or 1 hour 15 minutes.
Elastic Force Acceleration
- what is the speed of the time machine
How to find mass?
Many of us in school time wondered: "How to find body weight"? Now we will try to answer this question.
Finding mass in terms of its volume
Suppose you have a barrel of two hundred liters at your disposal. You intend to fill it entirely with the diesel fuel you use to heat your small boiler house. How to find the mass of this barrel filled with diesel fuel? Let's try to solve this seemingly simple task together with you.
Solving the problem of how to find the mass of a substance in terms of its volume is quite easy. To do this, apply the formula for the specific density of a substance
where p is the specific gravity of the substance;
m - its mass;
v - occupied volume.
Grams, kilograms and tons will be used as a measure of mass. Measures of volume: cubic centimeters, decimeters and meters. Specific gravity will be calculated in kg/dm³, kg/m³, g/cm³, t/m³.
Thus, in accordance with the conditions of the problem, we have a barrel with a volume of two hundred liters at our disposal. This means that its volume is 2 m³.
But you want to know how to find the mass. From the above formula, it is derived as follows:
First we need to find the value of p - the specific gravity of diesel fuel. You can find this value using the directory.
In the book we find that p = 860.0 kg/m³.
Then we substitute the obtained values into the formula:
m = 860 * 2 = 1720.0 (kg)
Thus, the answer to the question of how to find the mass was found. One ton and seven hundred and twenty kilograms is the weight of two hundred liters of summer diesel fuel. Then you can make an approximate calculation of the total weight of the barrel and the capacity of the rack for the solarium barrel in the same way.
Finding mass through density and volume
Very often in practical tasks in physics one can meet such quantities as mass, density and volume. In order to solve the problem of how to find the mass of a body, you need to know its volume and density.
Items you will need:
1) Roulette.
2) Calculator (computer).
3) Capacity for measurement.
4) Ruler.
It is known that objects with the same volume, but made of different materials, will have different masses (for example, metal and wood). The masses of bodies that are made of a certain material (without voids) are directly proportional to the volume of the objects in question. Otherwise, a constant is the ratio of the mass to the volume of an object. This indicator is called the "density of the substance." We will refer to it as d.
Now it is required to solve the problem of how to find the mass in accordance with the formula d = m/V, where
m is the mass of the object (in kilograms),
V is its volume (in cubic meters).
Thus, the density of a substance is the mass per unit of its volume.
If you need to find the density of the material from which an object is made, then you should use the density table, which can be found in a standard physics textbook.
The volume of an object is calculated by the formula V = h * S, where
V - volume (m³),
H is the height of the object (m),
S is the base area of the object (m²).
In the event that you cannot clearly measure the geometric parameters of the body, then you should resort to the help of the laws of Archimedes. To do this, you will need a vessel that has a scale that serves to measure the volume of liquids and lower the object into water, that is, into a vessel that has divisions. The volume by which the contents of the vessel will be increased is the volume of the body that is immersed in it.
Knowing the volume V and the density d of an object, you can easily find its mass using the formula m = d * V. Before calculating the mass, you need to bring all measuring units into a single system, for example, into the SI system, which is an international measuring system.
In accordance with the above formulas, the following conclusion can be drawn: to find the required mass value with a known volume and a known density, it is required to multiply the density value of the material from which the body is made by the volume of the body.
Calculation of body mass and volume
In order to determine the density of a substance, it is necessary to divide the mass of the body by its volume:
Body weight can be determined using scales. How to find the volume of a body?
If the body has the shape of a rectangular parallelepiped (Fig. 24), then its volume is found by the formula
If it has some other form, then its volume can be found by the method that was discovered by the ancient Greek scientist Archimedes in the 3rd century BC. BC e.
Archimedes was born in Syracuse on the island of Sicily. His father, the astronomer Phidias, was a relative of Hieron, who became in 270 BC. e. the king of the city in which they lived.
Not all of Archimedes' writings have come down to us. Many of his discoveries became known thanks to later authors, whose surviving works describe his inventions. So, for example, the Roman architect Vitruvius (1st century BC) in one of his writings told the following story: with boundless wit. During his reign in Syracuse, Hieron, after the successful completion of all his activities, vowed to donate a golden crown to the immortal gods in some temple. He agreed with the master on a high price for the work and gave him the amount of gold he needed by weight. On the appointed day, the master brought his work to the king, who found it excellently executed; after weighing, the weight of the crown was found to correspond to the given weight of gold.
After that, a denunciation was made that part of the gold was taken from the crown and the same amount of silver was mixed in instead. Hiero was angry that he had been tricked, and, not finding a way to convict this theft, asked Archimedes to think carefully about it. He, immersed in thoughts on this issue, somehow accidentally came to the bathhouse and there, sinking into the bath, noticed that such an amount of water was flowing out of it, what was the volume of his body immersed in the bath. Finding out for himself the value of this fact, he, without hesitation, jumped out of the bath with joy, went home naked and in a loud voice told everyone that he had found what he was looking for. He ran and shouted the same thing in Greek: “Eureka, Eureka! (Found, found!)
Then, Vitruvius writes, Archimedes took a vessel filled to the brim with water and lowered into it a gold ingot equal in weight to a crown. After measuring the volume of water displaced, he again filled the vessel with water and lowered the crown into it. The volume of water displaced by the crown turned out to be greater than the volume of water displaced by the gold ingot. The larger volume of the crown meant that it contained a substance less dense than gold. Therefore, the experiment done by Archimedes showed that part of the gold was stolen.
So, to determine the volume of a body that has an irregular shape, it is enough to measure the volume of water displaced by this body. With a measuring cylinder (beaker), this is easy to do.
In cases where the mass and density of the body are known, its volume can be found by the formula following from formula (10.1):
This shows that to determine the volume of a body, it is necessary to divide the mass of this body by its density.
If, on the contrary, the volume of the body is known, then, knowing what substance it consists of, you can find its mass:
To determine the mass of a body, it is necessary to multiply the density of the body by its volume.
1. What methods of volume determination do you know? 2. What do you know about Archimedes? 3. How can you find the mass of a body by its density and volume? Experimental task. Take a bar of soap that has the shape of a rectangular parallelepiped, on which its mass is indicated. After making the necessary measurements, determine the density of the soap.
Gravity is the amount by which a body is attracted to the earth under the influence of its attraction. This indicator directly depends on the weight of a person or the mass of an object. The more weight, the higher it is. In this article, we will explain how to find the force of gravity.
From a school physics course: the force of gravity is directly proportional to the weight of the body. You can calculate the value using the formula F \u003d m * g, where g is a coefficient equal to 9.8 m / s 2. Accordingly, for a person who weighs 100 kg, the force of attraction is 980. It is worth noting that in practice everything is a little different, and many factors affect gravity.Factors affecting gravity:
- distance from the ground;
- the geographical location of the body;
- Times of Day.
If the body is not dragged in a horizontal direction, then it is worth taking into account the angle at which the object deviates from the horizon. As a result, the formula will look like this: F=m*g – Fthrust*sin. The force of gravity is measured in newtons. For calculations, use the speed measured in m/s. To do this, divide the speed in km/h by 3.6.
