Momentum - AP Physics C: Electricity and Magnetism
Card 1 of 176
In an elastic collision, what combination of quantities is conserved?
In an elastic collision, what combination of quantities is conserved?
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The primary difference between elastic and inelastic collisions is the conservation of kinetic energy. Kinetic energy is conserved in elastic collisions, but is not conserved in inelastic collisions. Momentum is always conserved, regardless of collision type. Mass is conserved regardless of collision type as well, but the mass may be deformed by an inelastic collision, resulting in the two original masses being stuck together.
There is no description in the problem reagrding position, so we cannot comment on potential energy.
The primary difference between elastic and inelastic collisions is the conservation of kinetic energy. Kinetic energy is conserved in elastic collisions, but is not conserved in inelastic collisions. Momentum is always conserved, regardless of collision type. Mass is conserved regardless of collision type as well, but the mass may be deformed by an inelastic collision, resulting in the two original masses being stuck together.
There is no description in the problem reagrding position, so we cannot comment on potential energy.
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A 200kg car is traveling west at 
. It collides with a 150kg car that was at rest. Following the collision, the second car moves with a velocity of 
west. Assuming that the collision is elastic, what is the velocity of the first car after the collision?
A 200kg car is traveling west at
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The collision is assumed to be elastic, so both momentum and kinetic energy are conserved. Use the law of conservation of momentum:
Momentum is the product of velocity and mass:
We can expand the summation for the initial and final conditions:
Use the given values to fill in the equation and solve for 
:
Since the final velocity is positive, we know that the car is still traveling toward the west.
The collision is assumed to be elastic, so both momentum and kinetic energy are conserved. Use the law of conservation of momentum:
Momentum is the product of velocity and mass:
We can expand the summation for the initial and final conditions:
Use the given values to fill in the equation and solve for
Since the final velocity is positive, we know that the car is still traveling toward the west.
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In an inelastic collision, which combination of quantities is conserved?
In an inelastic collision, which combination of quantities is conserved?
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In a perfectly inelastic collision, the two colliding objects stick together; the two colliding objects deform, but mass is still conserved. Momentum is conserved during collisions of any sort, including inelastic collisions.
Kinetic energy is reduced during an inelastic collision, and is only conserved in elastic collisions. During inelastic collisions, some kinetic energy is lost to the environment in the form of heat or sound.
The problem does not give any information regarding position, and thus we cannot comment on any changes or lack of changes in potential energy.
In a perfectly inelastic collision, the two colliding objects stick together; the two colliding objects deform, but mass is still conserved. Momentum is conserved during collisions of any sort, including inelastic collisions.
Kinetic energy is reduced during an inelastic collision, and is only conserved in elastic collisions. During inelastic collisions, some kinetic energy is lost to the environment in the form of heat or sound.
The problem does not give any information regarding position, and thus we cannot comment on any changes or lack of changes in potential energy.
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Two train cars, each with a mass of 2400 kg, are traveling along the same track. One car is traveling with a velocity of 
east, while the other travels with a velocity of 
west. The two cars collide and stick together as one mass. What is the magnitude and direction of the resulting velocity?
Two train cars, each with a mass of 2400 kg, are traveling along the same track. One car is traveling with a velocity of
Tap to reveal answer
Use the law of conservation of momentum:
Momentum is the product of velocity and mass:
We can expand the summation for the initial and final conditions:
Note that we are working with an inelastic collision, meaning that the two masses stick together after the collision. Because of this, they will have the same final velocity:
Use the given values to fill in the equation and solve for 
. Keep in mind that we must designate a positive direction and a negative direction. We will use east as positive and west as negative.
Since the final velocity is positive, we can determine that they train cars are traveling toward the east.
Use the law of conservation of momentum:
Momentum is the product of velocity and mass:
We can expand the summation for the initial and final conditions:
Note that we are working with an inelastic collision, meaning that the two masses stick together after the collision. Because of this, they will have the same final velocity:
Use the given values to fill in the equation and solve for
Since the final velocity is positive, we can determine that they train cars are traveling toward the east.
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A 
bullet is fired at 
at a block of wood that is moving in the opposite direction at a speed of 
. The bullet passes through the block and emerges with the speed of 
, while the block ends up at rest.
What is the mass of the block?
A
What is the mass of the block?
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This problem is a conservation of momentum problem. When doing these types of problems, the equation to jump to is:
It is given to us that 
is 
or 
, 
is 
, 
is unknown, 
is 
.
is 
and 
is 
.
With all this information given, the only unknown is 
.
Plugging everything in, we get:
This problem is a conservation of momentum problem. When doing these types of problems, the equation to jump to is:
It is given to us that
With all this information given, the only unknown is
Plugging everything in, we get:
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A pitcher throws a 0.15kg baseball at 
towards the batter and the batter hits the ball with his bat. The ball leaves the bat in the opposite direction at a speed of 
. Calculate the impulse experienced by the baseball.
A pitcher throws a 0.15kg baseball at
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To calculate the impulse, know that it is equal to the change in momentum.
Write the impulse equation in terms of mass and velocity.
In our case, the initial velocity of the baseball is 
and its final velocity is 
, where the negative sign indicates that the ball is traveling in the opposite direction. Also, m = 0.15kg. The impulse on the ball can be calculated below.
The negative sign tells that the force on the baseball is opposed to the original momentum.
To calculate the impulse, know that it is equal to the change in momentum.
Write the impulse equation in terms of mass and velocity.
In our case, the initial velocity of the baseball is
The negative sign tells that the force on the baseball is opposed to the original momentum.
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Which of the following could be used as units of impulse?
Which of the following could be used as units of impulse?
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Relevant equations:
Impulse is defined as change in momentum, so has the same units as momentum. These units can easily be found using the given equations.
Relevant equations:
Impulse is defined as change in momentum, so has the same units as momentum. These units can easily be found using the given equations.
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A baseball player hits a 
baseball initially moving at 
, returning it at a speed of 
along the same path. If the ball was in contact with the bat for 
, what magnitude of force did the ball experience during the moment of contact?
A baseball player hits a
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Relevant equations:
Evaluate the impulse based on the mass and change of velocity.
Use the total impulse and time in the second equation.
Solve for the average force.
Relevant equations:
Evaluate the impulse based on the mass and change of velocity.
Use the total impulse and time in the second equation.
Solve for the average force.
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In an elastic collision, what combination of quantities is conserved?
In an elastic collision, what combination of quantities is conserved?
Tap to reveal answer
The primary difference between elastic and inelastic collisions is the conservation of kinetic energy. Kinetic energy is conserved in elastic collisions, but is not conserved in inelastic collisions. Momentum is always conserved, regardless of collision type. Mass is conserved regardless of collision type as well, but the mass may be deformed by an inelastic collision, resulting in the two original masses being stuck together.
There is no description in the problem reagrding position, so we cannot comment on potential energy.
The primary difference between elastic and inelastic collisions is the conservation of kinetic energy. Kinetic energy is conserved in elastic collisions, but is not conserved in inelastic collisions. Momentum is always conserved, regardless of collision type. Mass is conserved regardless of collision type as well, but the mass may be deformed by an inelastic collision, resulting in the two original masses being stuck together.
There is no description in the problem reagrding position, so we cannot comment on potential energy.
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A 200kg car is traveling west at . It collides with a 150kg car that was at rest. Following the collision, the second car moves with a velocity of west. Assuming that the collision is elastic, what is the velocity of the first car after the collision?
A 200kg car is traveling west at
Tap to reveal answer
The collision is assumed to be elastic, so both momentum and kinetic energy are conserved. Use the law of conservation of momentum:
Momentum is the product of velocity and mass:
We can expand the summation for the initial and final conditions:
Use the given values to fill in the equation and solve for :
Since the final velocity is positive, we know that the car is still traveling toward the west.
The collision is assumed to be elastic, so both momentum and kinetic energy are conserved. Use the law of conservation of momentum:
Momentum is the product of velocity and mass:
We can expand the summation for the initial and final conditions:
Use the given values to fill in the equation and solve for
Since the final velocity is positive, we know that the car is still traveling toward the west.
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In an inelastic collision, which combination of quantities is conserved?
In an inelastic collision, which combination of quantities is conserved?
Tap to reveal answer
In a perfectly inelastic collision, the two colliding objects stick together; the two colliding objects deform, but mass is still conserved. Momentum is conserved during collisions of any sort, including inelastic collisions.
Kinetic energy is reduced during an inelastic collision, and is only conserved in elastic collisions. During inelastic collisions, some kinetic energy is lost to the environment in the form of heat or sound.
The problem does not give any information regarding position, and thus we cannot comment on any changes or lack of changes in potential energy.
In a perfectly inelastic collision, the two colliding objects stick together; the two colliding objects deform, but mass is still conserved. Momentum is conserved during collisions of any sort, including inelastic collisions.
Kinetic energy is reduced during an inelastic collision, and is only conserved in elastic collisions. During inelastic collisions, some kinetic energy is lost to the environment in the form of heat or sound.
The problem does not give any information regarding position, and thus we cannot comment on any changes or lack of changes in potential energy.
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Two train cars, each with a mass of 2400 kg, are traveling along the same track. One car is traveling with a velocity of east, while the other travels with a velocity of west. The two cars collide and stick together as one mass. What is the magnitude and direction of the resulting velocity?
Two train cars, each with a mass of 2400 kg, are traveling along the same track. One car is traveling with a velocity of
Tap to reveal answer
Use the law of conservation of momentum:
Momentum is the product of velocity and mass:
We can expand the summation for the initial and final conditions:
Note that we are working with an inelastic collision, meaning that the two masses stick together after the collision. Because of this, they will have the same final velocity:
Use the given values to fill in the equation and solve for . Keep in mind that we must designate a positive direction and a negative direction. We will use east as positive and west as negative.
Since the final velocity is positive, we can determine that they train cars are traveling toward the east.
Use the law of conservation of momentum:
Momentum is the product of velocity and mass:
We can expand the summation for the initial and final conditions:
Note that we are working with an inelastic collision, meaning that the two masses stick together after the collision. Because of this, they will have the same final velocity:
Use the given values to fill in the equation and solve for
Since the final velocity is positive, we can determine that they train cars are traveling toward the east.
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A bullet is fired at at a block of wood that is moving in the opposite direction at a speed of . The bullet passes through the block and emerges with the speed of , while the block ends up at rest.
What is the mass of the block?
A
What is the mass of the block?
Tap to reveal answer
This problem is a conservation of momentum problem. When doing these types of problems, the equation to jump to is:
It is given to us that is or , is , is unknown, is .
is and is .
With all this information given, the only unknown is .
Plugging everything in, we get:
This problem is a conservation of momentum problem. When doing these types of problems, the equation to jump to is:
It is given to us that
With all this information given, the only unknown is
Plugging everything in, we get:
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We have two balls. The first ball has mass 0.54kg and is traveling 7.1m/s to the right. It collides head-on elastically with a second ball of mass 0.95kg traveling 2.8m/s to the left. After the collision, what is the speed and direction of each ball?
We have two balls. The first ball has mass 0.54kg and is traveling 7.1m/s to the right. It collides head-on elastically with a second ball of mass 0.95kg traveling 2.8m/s to the left. After the collision, what is the speed and direction of each ball?
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We must use conservation of momentum to tackle this problem.
We are to find 
and 
, the velocities of the balls after the collision. We know the following for the first ball:
and we know the following for the second ball:
.
After plugging these values into our conservation of momentum equation, it is clear that we can't use this equation alone to find 
and 
; however, since we are dealing with an elastic collision, we can use the relation below.
This relation can be derived using conservation of momentum and conservation of kinetic energy equations. Remember that kinetic energy is only conserved if the collision is elastic. We can use this relation to eliminate either 
or 
in our conservation of momentum equation.
Plug this into our conservation of momentum equation.
So now 
is eliminated and we can solve for 
.
This is the speed of the second ball, and it is traveling to the right because of the positive value. Use this positive value to find 
by using the relation we found earlier.
This is the speed of the first ball and it is traveling to the left due to the negative sign.
We must use conservation of momentum to tackle this problem.
We are to find
and we know the following for the second ball:
After plugging these values into our conservation of momentum equation, it is clear that we can't use this equation alone to find
This relation can be derived using conservation of momentum and conservation of kinetic energy equations. Remember that kinetic energy is only conserved if the collision is elastic. We can use this relation to eliminate either
Plug this into our conservation of momentum equation.
So now
This is the speed of the second ball, and it is traveling to the right because of the positive value. Use this positive value to find
This is the speed of the first ball and it is traveling to the left due to the negative sign.
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A 30kg cart travels at 9m/s and it hits another cart of mass 46kg traveling at 4m/s in the opposite direction. After the collision, they stick together to form one cart. Find the speed of this cart
A 30kg cart travels at 9m/s and it hits another cart of mass 46kg traveling at 4m/s in the opposite direction. After the collision, they stick together to form one cart. Find the speed of this cart
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For the 30 kg cart, we know
and for the 46 g cart, we know
.
After the collision, we have 
.
Use conservation of momentum to solve this problem.
For the 30 kg cart, we know
and for the 46 g cart, we know
After the collision, we have
Use conservation of momentum to solve this problem.
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There are two skaters. The male skater with mass 68kg travels 15m/s North. He approaches a 60kg female skater who is travel 12m/s East; they approach each other at right angles. When they meet, they hold on to each other. At what direction and speed do they move after they meet?
There are two skaters. The male skater with mass 68kg travels 15m/s North. He approaches a 60kg female skater who is travel 12m/s East; they approach each other at right angles. When they meet, they hold on to each other. At what direction and speed do they move after they meet?
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This is a two-dimensional inelastic collision problem and we use conservation of momentum to solve. We know the following.
Male skater: 
, 
Female skater: 
,
First, write down two equations representing conservation of momentum. One equation represents momentum in the x-direction (East-West direction), which is 
,and the other gives the momentum in the y-direction (North-South direction), 
.
Take the y-direction of momentum and divide it by the x-direction momentum.
Simplify.
Plug in the numbers to find the angle
To find the speed at which they move at this angle we can use one of the momentum equations.
Solve for v.
This is a two-dimensional inelastic collision problem and we use conservation of momentum to solve. We know the following.
Male skater:
Female skater:
First, write down two equations representing conservation of momentum. One equation represents momentum in the x-direction (East-West direction), which is
Take the y-direction of momentum and divide it by the x-direction momentum.
Simplify.
Plug in the numbers to find the angle
To find the speed at which they move at this angle we can use one of the momentum equations.
Solve for v.
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Object A has mass 
and initially moves to the right at 
. It then collides with object B, which has mass 
and was initially moving to the right at 
. If the two objects stick together after the collision, what percentage of the initial kinetic energy has been dissipated?
Object A has mass
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Relevant equations:
Use conservation of momentum to determine the final velocity of the objects.
Calculate the total initial kinetic energy of the two objects.
Calculate the total final kinetic energy of the two objects.
Find the difference in kinetic energy.
This is the amount of kinetic energy lost during the inelastic collision. Express this amount as a percentage of the initial kinetic energy.
Relevant equations:
Use conservation of momentum to determine the final velocity of the objects.
Calculate the total initial kinetic energy of the two objects.
Calculate the total final kinetic energy of the two objects.
Find the difference in kinetic energy.
This is the amount of kinetic energy lost during the inelastic collision. Express this amount as a percentage of the initial kinetic energy.
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A pitcher throws a 0.15kg baseball at towards the batter and the batter hits the ball with his bat. The ball leaves the bat in the opposite direction at a speed of . Calculate the impulse experienced by the baseball.
A pitcher throws a 0.15kg baseball at
Tap to reveal answer
To calculate the impulse, know that it is equal to the change in momentum.
Write the impulse equation in terms of mass and velocity.
In our case, the initial velocity of the baseball is and its final velocity is , where the negative sign indicates that the ball is traveling in the opposite direction. Also, m = 0.15kg. The impulse on the ball can be calculated below.
The negative sign tells that the force on the baseball is opposed to the original momentum.
To calculate the impulse, know that it is equal to the change in momentum.
Write the impulse equation in terms of mass and velocity.
In our case, the initial velocity of the baseball is
The negative sign tells that the force on the baseball is opposed to the original momentum.
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Which of the following could be used as units of impulse?
Which of the following could be used as units of impulse?
Tap to reveal answer
Relevant equations:
Impulse is defined as change in momentum, so has the same units as momentum. These units can easily be found using the given equations.
Relevant equations:
Impulse is defined as change in momentum, so has the same units as momentum. These units can easily be found using the given equations.
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A baseball player hits a baseball initially moving at , returning it at a speed of along the same path. If the ball was in contact with the bat for , what magnitude of force did the ball experience during the moment of contact?
A baseball player hits a
Tap to reveal answer
Relevant equations:
Evaluate the impulse based on the mass and change of velocity.
Use the total impulse and time in the second equation.
Solve for the average force.
Relevant equations:
Evaluate the impulse based on the mass and change of velocity.
Use the total impulse and time in the second equation.
Solve for the average force.
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