As a result of the transition from one. The transition of a satellite from one orbit to another
Demo version of the exam 2019 - task number 6. An artificial satellite of the Earth has moved from one circular orbit to another, in the new orbit the speed of its movement is less than in the previous one. How did the potential energy of the satellite in the Earth's gravity field and its period of revolution around the Earth change?
1) increases
2) decreases
3) does not change
write down to the table
Answer: 11
Demo version USE 2018 - task number 6. As a result of the transition of the Earth's satellite from one circular orbit to another, the speed of its movement decreases. How does the centripetal acceleration of the satellite and the period of its revolution around the Earth change in this case?
For each value, determine the appropriate nature of the change:
1) increases
2) decreases
3) does not change
write down to the table selected numbers for each physical quantity.
Numbers in the answer may be repeated.
Solution:
1) Centripetal acceleration of the satellite: decreasing
⇒ a y ↓, F T
⇒ a y ↓, V 2 ↓, r
2) The period of revolution of the satellite around the Earth: increases
⇒ r , V ↓, T
Answer: 21
Demonstration version of the USE 2017 - task No. 6
flight altitude artificial satellite above the Earth increased from 400 to 500 km. How did the speed of the satellite and its potential energy change as a result of this?
For each value, determine the appropriate nature of the change:
1. increased
2. decreased
3. has not changed
Write down the selected numbers for each physical quantity. Numbers in the answer may be repeated.
Solution:
The force of attraction from the Earth acts on the satellite, it imparts centripetal acceleration to it:
R is the distance from the satellite to the center of the Earth, which has increased, as a result of which the speed of movement has decreased.
As the distance increased, the potential energy also increased.
Answer: 21
Demonstration version of the USE 2016 - task No. 6
A solid wooden block floats on the surface of the water. How will the immersion depth of the bar and the Archimedes force acting on the bar change if it is replaced by a solid bar of the same density and height, but of a larger mass?
For each value, determine the appropriate nature of the change:
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.
Solution:
The Archimedes force is the buoyant force acting on bodies immersed in a liquid,
where is the density of the liquid; - volume of the body; - acceleration of gravity.
The volume of the body is , where is the mass of the body; is the density of the body.
Substitute in the formula of Archimedes' force, we get: .
The last expression shows that the strength of Archimedes and the mass of the body depends in direct proportion, i.e. the greater the mass, the greater the strength of Archimedes. The depth will remain the same, because. depth does not depend on mass, but depends on the density of the body.
Task 6. As a result of the transition of an artificial Earth satellite from one circular orbit to another, its centripetal acceleration increases. How does this transition change the speed of the satellite in orbit and the period of its revolution around the Earth?
1) increases
2) decreases
3) does not change
Solution.
The only force acting on the satellite is the gravity of the earth.
where M is the mass of the earth; m is the mass of the satellite; R is the radius of the orbit. According to Newton's second law, we can write:
,
where a - plays the role of centripetal acceleration. This shows that as the acceleration increases, the radius of the orbit will decrease.
Now consider how the speed of the satellite will change depending on the radius of the orbit. Substitute instead of acceleration , we get:
.
That is, as R decreases, the speed of the satellite increases.
The orbital period of a satellite around the earth is the time it takes the satellite to make one revolution around the earth. If the radius of the orbit decreases and the centripetal acceleration increases, then the speed of the satellite increases. Thus, the satellite travels a shorter distance at a higher speed and its period decreases.
Answer: 12.
Task 6. A wooden block rests on a rough inclined plane. The angle of inclination of the plane was reduced. How did the static friction force acting on the bar and the coefficient of friction of the bar on the plane change in this case? For each value, determine the appropriate nature of the change:
1) increased
2) decreased
3) has not changed
Solution.
Since the block is at rest, the static friction force balances the sliding force of the block (tangential force). As the angle of inclination decreases, the tangential force decreases, therefore, in accordance with Newton's third law, the static friction force also decreases.
The coefficient of friction of the bar on the surface depends only on the material of the contacting planes and their area, that is, it will not change.
Answer: 23.
Task 6. A stone is thrown upwards at an angle to the horizon. Air resistance is negligible. How do the acceleration modulus of the stone and its potential energy in the gravitational field change when the stone moves upwards?
For each value, determine the appropriate nature of the change:
1) increases
2) decreases
3) does not change
Solution.
The projection of the movement of the stone on the Oy axis (vertical axis) can be written as
.
From this expression it can be seen that the acceleration of the stone is equal to g - the acceleration of free fall, that is, it does not change.
The potential energy of the stone is
and increases with increasing height, that is, when moving up, the potential energy increases.
Answer: 31.
Task 6. A massive load suspended from the ceiling on a spring makes vertical free vibrations. The spring remains stretched all the time. How does the potential energy of the load in the gravitational field and its velocity behave when the load moves upward from the equilibrium position?
For each value, determine the appropriate nature of the change:
1) increases
2) decreases
3) does not change
Solution.
The potential energy of the load is determined by the expression
where m is the weight of the cargo; h is the height of the load above ground level.
The problem says that the spring is stretched all the time and in this state the load moves up. It can be seen from the formula that the height of the load h increases, therefore, the potential energy of the load will also increase. The velocity v of the body will decrease as the load moves against gravity and gradually stops.
Answer: 12.
Task 6. The load of the spring pendulum shown in the figure performs free harmonic oscillations between points 1 and 3. How does the speed of the load and the stiffness of the spring change when the pendulum load moves from point 1 to point 2?
For each value, determine the appropriate nature of the change:
1) increases
2) decreases
3) does not change
Solution.
Since oscillations occur between points 1-3, then at point 1 the load has zero speed, and at point 2 the speed reaches its maximum value, that is, it increases. The stiffness of the spring depends on physical properties the spring itself and is a constant (unchanging) value.
Answer: 13.
Task 6. As a result of braking in the upper layers of the atmosphere, the flight altitude of the artificial satellite above the Earth decreased from 400 to 300 km. How did this change the speed of the satellite and its centripetal acceleration?
For each value, determine the appropriate nature of the change:
1) increased
2) decreased
3) has not changed
Solution.
According to the law gravity, the satellite will be attracted to the Earth with a force
where m is the mass of the satellite; M is the mass of the Earth; R is the radius of the satellite's orbit. According to Newton's second law, we can write that
where is the centripetal acceleration of the satellite. Combining these two expressions, we have:
It can be seen from this formula that as the orbit radius R decreases, the satellite's velocity v and its centripetal acceleration increase.
Answer: 11.
assignment 6. As a result of the transition of the Earth's satellite from one circular orbit to another, its centripetal acceleration decreases. How do the potential energy of the satellite in the Earth's gravity field and the speed of its movement in orbit change as a result of this transition?
For each value, determine the appropriate nature of the change:
1) increases
2) decreases
3) does not change
Solution.
An Earth satellite of mass m and an Earth of mass M are attracted to each other at a distance R with the force of universal gravitation
By Newton's second law this force can also be represented as
where is the centripetal acceleration of the satellite. Combining the equations, we have:
whence the radius of the orbit
It can be seen from the last formula that as the centripetal acceleration decreases, the radius of the orbit R of the satellite increases. Let us find how the potential energy of the satellite and the speed of its movement in orbit will change.
Centripetal acceleration can be written as , where v is the speed of the satellite, then
and its potential energy is defined as the gravitational energy due to the mutual attraction of the satellite and the Earth:
The last two formulas show that as R increases, the satellite's speed decreases and the potential energy increases (note the "-" sign in front of the satellite's potential energy formula).
Answer: 12.
Task 6. A massive load suspended from the ceiling on a spring performs vertical free vibrations. The spring remains stretched all the time. How does the potential energy of the spring and the speed of the load behave when the load moves downward from the equilibrium position?
For each value, determine the appropriate nature of the change:
1) increases
2) decreases
3) does not change
Solution.
The equilibrium position is the position with the maximum speed at oscillatory motion cargo. Therefore, when moving down from the equilibrium position, the speed of the load decreases.
The potential energy of the spring is proportional to the deformation of the spring and, moving down, the spring stretches and its potential energy increases.
Answer: 12.
Task 6. A body of mass m, moving translationally in an inertial frame of reference, is subjected to a constant resultant force F during the time ∆t. If the force acting on the body increases, how will the module of the momentum of the force and the module of change of the momentum of the body change during the same time interval ∆t?
1) increase
2) decrease
3) will not change
Solution.
With an increase in the force F=ma, the acceleration of the body also increases. An increase in acceleration results in an increase in speed. Therefore, the momentum of the body, which is equal, will also increase. The modulus of change in the momentum of the body will also increase, since the body moves with a constant acceleration, greater than before, and the value is proportional to the acceleration.
Answer: 11.
Task 6. A body of mass m, moving translationally in an inertial frame of reference, is subjected to a constant resultant force F during the time ∆t. If the force acting on the body decreases, how will the modulus of the force impulse and the modulus of the acceleration of the body change during the same time interval ∆t? For each value, determine the appropriate nature of the change:
1) increase
2) decrease
3) will not change
Solution.
When the force F=ma decreases, the acceleration of the body also decreases. The momentum modulus of the force, equal to the change in the momentum of the body, will decrease with decreasing acceleration, since the final velocity v will become smaller.
Answer: 22.
Task 6. A ball thrown horizontally from a height H with an initial velocity v0 travels a distance L in the horizontal direction in time t (see figure). What will happen with time and flight distance if the ball's initial velocity is doubled on the same setup? Ignore air resistance. For each quantity, determine the appropriate nature of its change:
1) increase
2) decrease
3) will not change
Solution.
The flight time of the ball will be equal to the time of its fall from a height H, since the initial vertical velocity is zero. Therefore, changing the initial horizontal speed ball 2 times, the flight time will remain the same.
With an increase in speed by 2 times and the same flight time, the length L \u003d vt will double.
Answer: 31.
Task 6. A steel ball hangs on a thread tied to a tripod. The ball is completely immersed in kerosene (Fig. 1). Then the glass with kerosene was replaced by a glass with water, and the ball was completely in the water (Fig. 2). How did the tension force of the thread and the Archimedes force acting on the ball change in this case?
For each quantity, determine the appropriate nature of its change:
1) increased
2) decreased
3) has not changed
Solution.
The modulus of the thread tension is equal to the resulting force acting on the ball. The ball is affected by the force of gravity mg and the buoyant force of Archimedes, directed in the opposite direction, that is, the resulting force, and hence the tension of the thread, are equal:
where V is the volume of the body immersed in the liquid; is the density of the liquid. Since the density of kerosene is kg/m3, and the density of water is kg/m3, the buoyancy force of Archimedes in the case of water is higher than with kerosene. Consequently, the tension of the thread when replacing kerosene with water will decrease, and the Archimedes force will increase.
Answer: 21.
Task 6. In the school laboratory, free oscillations of a spring pendulum are studied at various values of the mass of the pendulum. How will the period of its free oscillations and the period of change of its potential energy change if the mass of the pendulum is increased without changing the stiffness of the spring? For each value, determine the appropriate nature of the change:
1) increases
2) decreases
3) does not change
Solution.
The period of free oscillations of a spring pendulum with mass m and spring constant k is equal to . Therefore, with an increase in body mass m, the oscillation period will increase.
The potential energy of a spring pendulum is defined as , where x is the value of the spring deformation. It is easy to understand that with an increase in the mass of the pendulum, the extension of the spring x will increase, therefore, the period of change in the potential energy of the spring will also increase.
Answer: 11.
Task 6. From the top of an inclined plane, from a state of rest, a light box slides with acceleration, in which there is a load of mass m (see figure). How will the time of movement along an inclined plane and the modulus of work of gravity change if the same box with a load of mass m/2 slides from the same inclined plane?
For each value, determine the appropriate nature of the change:
1) increase
2) decrease
3) will not change
Solution.
In an inclined plane, the gravity of the box, created by the box, is equal to
and the friction force is opposite to it, equal to
The resultant force acting on the box in an inclined plane:
whence the acceleration of the box
The time it takes for the box to pass down the inclined plane can be found from the formula
where S is the length of the inclined plane.
The work of gravity is the quantity
Thus, with a decrease in the mass of the load m, the time of movement of the box along the inclined plane will remain the same, and the work of gravity will decrease.
Answer: 32.
Task 6. A solid wooden block floats on the surface of the water. How will the immersion depth of the bar and the Archimedes force acting on the bar change if it is replaced by a solid bar of the same density and height, but of a larger mass? For each value, determine the appropriate nature of the change:
1) increase
2) decrease
3) will not change
Solution.
If the bar has the same density and height, then the increase in mass can be carried out only by increasing its base area, and the depth of its immersion in water will remain the same.
The Archimedes force is defined as , where V is the volume of the part of the body immersed in water. Since this volume increases (the area of the bar has increased), then the strength of Archimedes will increase. The same conclusion can be drawn on the basis that the force of Archimedes must compensate for the force of gravity of the bar, and since its mass increases, the force of gravity mg will also increase.
Task number 1. -1 point
Two identical bars of thickness h, placed on top of each other, float in the water so that the water level falls on the border between them (see figure). By how much will the immersion depth change if one more bar is added to the stack?
Solution.
The solution is based on Newton's 2nd law. The force of gravity and the force of Archimedes act on the body. The body is in balance and
Therefore, the density of water is 2 times the density of the material of the bar. Thus, a bar of any size will sink exactly half: 3 bars will sink to a depth of 3h /2, i.e. the depth will change to h /2.
Task number 2. -2 points
As a result of the transition from one circular orbit to another, the centripetal acceleration of the Earth's satellite decreases. How do the radius of the satellite's orbit, the speed of its movement along the orbit and the period of revolution around the Earth change as a result of this transition?
Solution
In this problem, you also need to consider the forces that act on the body and write down Newton's 2nd law. The satellite is affected by the gravitational force from the Earth (gravitational forces from the rest of the bodies solar system- we neglect).
Newton's 2nd law:
From the last formula it is indeed clear that with a decrease in acceleration, the radius of the orbit - increases (the gravitational constant and the mass of the Earth are constants).
The centripetal acceleration formula can be used to analyze the change in speed:
Therefore, when moving to a higher orbit, the speed of the satellite decreases.
The period of revolution of the satellite - with an increase in R also increases:
Task number 3. -3 points
A piece of ice having a temperature of 0°C is placed in a calorimeter with an electric heater. To turn this ice into water at a temperature of 12 ° C, an amount of heat equal to 80 kJ is required. What temperature will be established inside the calorimeter if the ice receives from the heater an amount of heat equal to 60 kJ? Ignore the heat capacity of the calorimeter and heat exchange with the environment.
Solution
In this problem, it is very important to understand that the ice does not just heat up, but first melts, and only then heats up. The amount of heat spent on these processes
Task number 4. -1 point
The figure shows graphs of temperature changes of four bodies of the same mass as they absorb energy. At the initial moment of time, the bodies were in a solid state. Which of the graphs corresponds solid body with the lowest heat capacity? Why?
Task number 5. -1 point
The dew point for water vapor in the room is 6 o C. A dry bottle of water was brought into the room from the balcony. Soon it was covered with small drops of water. Why?
Solution
If, at a given humidity in the room, the temperature outside is less than 6 degrees, then water vapor near the surface of the bottle brought into the room becomes supersaturated and therefore condenses.
Task number 6. -3 points
Task number 7. -1 point
Point B is in the middle of segment AC. motionless point charges+q and -2q are located at points A and C, respectively (see figure). What charge should be placed at point C instead of charge -2q so that the tension electric field at point B doubled?
Task number 8. -2 points
With one resistance of the rheostat, the voltmeter shows 6 V, the ammeter - 1 A (see figure). With a different resistance of the rheostat, the reading of the devices is 4 V and 2A. What is the internal resistance and emf of the current source?
Solution
The voltmeter in this case shows the voltage both on the rheostat and on the current source, taking into account its internal resistance. This also follows from Ohm's law for a complete circuit.
In task No. 6 of the Unified State Exam in physics, it is necessary to choose the correct conclusion by analyzing the condition of the problem. The topic of the tasks is mechanics.
Theory for assignment No. 6 USE in physics
We briefly recall the main points.
According to Newton's second law, the force acting on a body is F=ma
The force of gravity is determined by the formula:
Here M and m are the masses of interacting (attracting) bodies, G is the gravitational constant. R is the distance between these bodies or between their centers, if the dimensions of the bodies are commensurate with the distance between them (the 2nd option corresponds, for example, to the situation when the Earth and its satellite are considered).
When moving in a circle, centripetal acceleration can be calculated by the formula:
The period of revolution of the satellite around the orbit is:
Archimedes' law: a force F=ρgV acts on a body immersed in water.
The kinetic energy of a body that oscillates is expressed by the formula:
The law of conservation of energy: the mechanical energy of a body does not change unless it is converted into internal energy.
Analysis of typical tasks No. 6 USE in physics
Demo version 2018
As a result of the transition of the Earth's satellite from one circular orbit to another, the speed of its movement decreases. How will the centripetal acceleration of the satellite and the period of revolution around the Earth change in this case?
- increases;
- Decreases;
- Doesn't change
Write in the table the selected numbers for each physical quantity. Numbers in the answer may be repeated.
Solution algorithm:
- Determine the forces acting on the satellite. We write down the corresponding formulas.
- We express the speed of the satellite in terms of the radius of the orbit and draw a conclusion regarding its change. We express the centripetal acceleration in terms of the radius of the orbit.
- We express the period of revolution of the satellite in terms of the radius of the orbit.
- We write down the answers.
Solution:
1. The Earth's gravity force F acts on the satellite. It is she who keeps the satellite in orbit. We denote the mass of the satellite m, the mass of the Earth - M. Then their interaction looks like this:
According to Newton's second law, the force F acting on the satellite is determined by the formula:
F=ma. But this same force is the force of mutual attraction:
Since the satellite is moving in a circular orbit, the acceleration a is centripetal. It can be determined by the formula:
So the strength F is equal to:
This formula expresses the dependence of the satellite's speed on the radius of the orbit.
According to the condition, the satellite changed its orbit, and it is known that the speed decreases. It follows from the formula for v that, at constant G and M, the speed and radius R are inversely proportional. This means that as the speed decreases, the radius increases. The radius is related to acceleration through the equation:
After reducing the mass in it, we get that the acceleration is inversely proportional to the radius. This means that as the radius increases, the acceleration decreases. Therefore, it is necessary to record in the table that the centripetal acceleration of the satellite decreases. Answer option - 2.
3. The time of a complete revolution (period) of the satellite in orbit is
In the formula, the period is directly proportional to the radius of the orbit and inversely proportional to the speed. If the radius has increased (see item 2), then the period has also increased. Answer option - 1.
4. Fill in the table:
The first version of the task (Demidova, No. 1)
A wooden block floats on the surface of kerosene, partially immersed in a liquid. How will the Archimedes force acting on the bar and the depth of the bar's immersion change if it floats in water?
For each value, determine the appropriate nature of the change:
1) increase
2) decrease
3) will not change
Solution algorithm:
- We analyze the condition of the problem.
- Compare the densities of kerosene and water. We draw a conclusion regarding the depth of immersion.
- We write down the answer.
Solution:
1. By condition, the bar floats with each of the indicated liquids. This suggests that the buoyancy force balances the force of gravity of the bar and is equal to it. The force of gravity does not change. Therefore, the strength of Archimedes will not change either. Answer option - 3.
2. The density of kerosene is less than the density of water. Since F A =ρgV, then at constant values of g and V, the Archimedes force is proportional to the density. Consequently, the Archimedes force in kerosene will be less than in water, and the block in water will be pushed out more strongly. This means that the bar sinks deeper in kerosene than in water. Those. depth will decrease in water. Answer option - 2.
The second version of the task (Demidova, No. 3)
Iron solid weight perfect gives small free vibrations on a light inextensible thread. This weight was then replaced with a solid aluminum weight of the same dimensions. The oscillation amplitude is the same in both cases. How will the oscillation period and the maximum kinetic energy of the weight change in this case?
For each value, determine the appropriate nature of the change:
1) increase
2) decrease
3) will not change
Algorithm for solving the problem:
- We analyze the condition of the problem. Compare the oscillation period.
- Compare the kinetic energy of the balls.
- We analyze the change in the oscillation period.
- We write down the answer.
Solution:
1. If the oscillation amplitude is constant, then this means that the weights deviate upward from the equilibrium position to the same height. The free fall acceleration g does not depend on the mass of the falling body. This means that the weights in at the same time reach the equilibrium point of the pendulum. That is, the period of their oscillations will be the same, i.e. Will not change. Answer option - 3.
2. The kinetic energy of the weight reaches its maximum when the weight passes the equilibrium point. This energy is
The oscillation period of the weights has not changed. Therefore, their speed is also the same. From this we conclude: the difference in the kinetic energies of the loads will differ by their mass. And since the mass of the aluminum weight is less, then its energy will be less. Answer option - 2.
The third version of the task (Demidova, No. 7)
The boy threw a steel ball upward at an angle to the horizon. Neglecting air resistance, determine how the total mechanical energy of the ball and the modulus of the vertical component of its velocity change as it approaches the ground.
For each value, determine the appropriate nature of the change:
1) increases
2) decreases
3) does not change
Solution algorithm:
- We analyze the condition of the problem.
- Break down the speed into components.
- We determine the nature of the change in the total mechanical energy.
- We write down the answer.
Solution:
1. A ball is thrown at an angle to the horizon. This means that its speed can be decomposed into two components - projections onto the selected coordinate axes. In this case, air resistance can be neglected.
2. The horizontal component of the ball's velocity during such a throw is constant, since there is no horizontal component of acceleration (there is only vertically downward g). And the vertical first decreases to zero (when the highest point of ascent is reached), and then increases as it approaches the ground (since the direction of movement coincides with the direction of acceleration g). Answer option - 1.
3. If the speed changes when moving down, then the kinetic energy of the ball also changes, reaching its maximum value at the moment it touches the ground. The potential energy changes from the greatest value v highest point rise to zero at the moment the ball touches the ground. But since air resistance can be neglected, the law of conservation of energy works, according to which the total mechanical energy does not change. Answer option - 3.
