Work and Energy - Physics
Card 0 of 44
A toy car is set up on a frictionless track containing a downward sloping ramp and a vertically oriented loop. Assume the ramp is 
tall. The car starts at the top of the ramp at rest.
What additional piece of information is necessary to calculate the maximum height of the loop if the car is to complete the loop and continue out the other side?
A toy car is set up on a frictionless track containing a downward sloping ramp and a vertically oriented loop. Assume the ramp is
What additional piece of information is necessary to calculate the maximum height of the loop if the car is to complete the loop and continue out the other side?
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This is an example of conservation of energy. The car starts at the top of the ramp, at height 
. It has no velocity at this time since it is starting from a rest. Therefore its total energy is 
where 
is the mass of the car and 
is the value of gravitational acceleration.
At the bottom of the loop, all of the potential energy will have been converted into kinetic energy.
As the car traverses the loop and rises above the ground, kinetic energy will be converted back into potential energy. The shape of the loop does not matter in this case -- only the vertical distance between the ground and the car.
In the tallest possible loop, all kinetic energy at the bottom is converted to potential energy at the top. This is the maximum height the car can reach -- there is no additional energy left to continue climbing a taller loop. Therefore, the potential energy at the top of the tallest loop we can build is equal to the kinetic energy at the bottom of the loop. But we have already noted that the kinetic energy at the bottom of the loop is equal to the potential energy at the top of the ramp.
Therefore, we set 
. We see that 
and 
cancel, and we are left with 
. In other words, the tallest loop you can build is equal to the height of whatever ramp you select. In this example, the tallest loop we can build is 
. We do not need to know the specific values of 
or 
.
This is an example of conservation of energy. The car starts at the top of the ramp, at height
At the bottom of the loop, all of the potential energy will have been converted into kinetic energy.
As the car traverses the loop and rises above the ground, kinetic energy will be converted back into potential energy. The shape of the loop does not matter in this case -- only the vertical distance between the ground and the car.
In the tallest possible loop, all kinetic energy at the bottom is converted to potential energy at the top. This is the maximum height the car can reach -- there is no additional energy left to continue climbing a taller loop. Therefore, the potential energy at the top of the tallest loop we can build is equal to the kinetic energy at the bottom of the loop. But we have already noted that the kinetic energy at the bottom of the loop is equal to the potential energy at the top of the ramp.
Therefore, we set
An elevator is designed to hold 
of cargo. The designers want the elevator to be able to go from the ground floor to the top of a 
tall building in 
. What is the minimum amount of power that must be delivered to the motor at the top of the shaft? Assume no friction and that the elevator itself has a negligible weight.
An elevator is designed to hold
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Power is the rate of energy transfer. To raise a 
object 
, a total of 
or (
is required. To find the power in Watts (
), we divide the total energy required by the time over which the energy must be transferred:
Power is the rate of energy transfer. To raise a
How far can a person jump while running at 
and a vertical velocity of 
?
How far can a person jump while running at
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We know that:
and we are looking for the maximum height (vertical displacement) this person can obtain, so we aren't concerned with 
.
We can apply the conservation of energy:
Masses cancel, so
Solve for 
:
(rounded to simplify our calculations)
so let's plug in what we know
. This is our final answer.
We know that:
and we are looking for the maximum height (vertical displacement) this person can obtain, so we aren't concerned with
We can apply the conservation of energy:
Masses cancel, so
Solve for
so let's plug in what we know
If a 
object has a kinetic energy of 
right after it is launched in the air, and it has 
KE at its max height, what is its max height?
If a
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Let's first write down the information we are given:
In order to solve this problem we must apply the conservation of energy, which states 
since no friction.
This means that as the project reaches its max height energy is converted from Kinetic Energy (energy of motion) to potential gravitational energy (based off of height).
We can subtract 
from 
to get the 
at its max height
=
so we can solve for the height
where 
therefore 
Let's first write down the information we are given:
In order to solve this problem we must apply the conservation of energy, which states
This means that as the project reaches its max height energy is converted from Kinetic Energy (energy of motion) to potential gravitational energy (based off of height).
We can subtract
so we can solve for the height
where
therefore
If an object has a kinetic energy of 
right after it is launched in the air, and it has 
KE at its max height of 
, what is the object's mass?
If an object has a kinetic energy of
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Let's first write down the information we are given:
In order to solve this problem we must apply the conservation of energy, which states since no friction.
This means that as the project reaches its max height energy is converted from Kinetic energy (energy of motion) to potential gravitational energy (based off of height).
We can subtract from to get the at its max height
=
so we can solve for the mass
where 
therefore 
Let's first write down the information we are given:
In order to solve this problem we must apply the conservation of energy, which states
This means that as the project reaches its max height energy is converted from Kinetic energy (energy of motion) to potential gravitational energy (based off of height).
We can subtract
so we can solve for the mass
where
therefore
A baseball weighing 
is dropped from a second story window which is 
high. What is the gravitational potential energy?
A baseball weighing
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Gravitational potential energy is given by the equation:
We are given all the information needed to solve for the potential energy.
Plug in known values and solve.
Recall that the units for energy are Joules. Newtons is the unit for force.
Gravitational potential energy is given by the equation:
We are given all the information needed to solve for the potential energy.
Plug in known values and solve.
Recall that the units for energy are Joules. Newtons is the unit for force.
A 
bowling ball is released from 
in the air. What is it's gravitation potential energy upon release?
A
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The equation for gravitational potential energy is:
We are given all the information needed to answer the question.
Plug in known values and solve.
The equation for gravitational potential energy is:
We are given all the information needed to answer the question.
Plug in known values and solve.
A 
bouncy ball is dropped from 
. When it bounces back up is reaches a height of 
. How much energy was loss?
A
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The formula for gravitational potential energy is:
To find the potential energy lost, we need to find the potential energy of the ball at two heights, then find the difference.
Note that the energy was not actually lost; rather, it was converted to kinetic energy.
The formula for gravitational potential energy is:
To find the potential energy lost, we need to find the potential energy of the ball at two heights, then find the difference.
Note that the energy was not actually lost; rather, it was converted to kinetic energy.
A car traveling at 
has a kinetic energy 
. If the car accelerates to 
, what will the new kinetic energy be?
A car traveling at
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Kinetic energy is given by
. We will begin by calculating the car's initial kinetic energy, in terms of the unknown mass of the car 
:
.
Next, we will calculate the final energy of the car, also in terms of the unknown mass of the car:
.
To find the ratio of the final to initial kinetic energy, we divide 
by 
. We see that this reduces to 
with the both the mass 
and 
terms cancelling. 
. Thus, the new kinetic energy is 
.
Kinetic energy is given by
Next, we will calculate the final energy of the car, also in terms of the unknown mass of the car:
To find the ratio of the final to initial kinetic energy, we divide
A 
steel ball is in a spring loaded launcher. The spring has a constant of 
. If the ball is pulled back 50 cm then released and the ball leaves the launcher at a speed of 
, how much work was done by friction?
A
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So in order to solve this problem, we first should think about where all the energy in the system is coming from and going. Specifically when you pull the spring back, the work you do is turned into potential energy stored in the spring. So:
and the energy transforms into kinetic when you let go, but some of that energy is lost to friction so
and 
So use the equation below, enter in your known quantities and then solve for the work done by friction.
Plug in known values and solve.
So in order to solve this problem, we first should think about where all the energy in the system is coming from and going. Specifically when you pull the spring back, the work you do is turned into potential energy stored in the spring. So:
and the energy transforms into kinetic when you let go, but some of that energy is lost to friction so
So use the equation below, enter in your known quantities and then solve for the work done by friction.
Plug in known values and solve.
Suppose that an object of mass 
is travelling towards a massless spring with a velocity 
. If the maximum displacement of the spring is 
, which of the following gives an expression for the spring constant, 
?
Note: Assume that there is no friction.
Suppose that an object of mass
Note: Assume that there is no friction.
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For this question, we're told than an object is travelling with a certain velocity towards a spring. After colliding with the spring and causing it to undergo a maximum displacement, we're asked to provide an expression for the spring constant.
In order to answer this question, we'll need to consider the energy of the object and the spring during the process described. First, the object is moving with a certain velocity towards the spring. Thus, the object has kinetic energy. When the object collides with the spring and displaces the spring to its maximum displacement, there will be a brief instant where the object has completely stopped moving. At this point, all of the block's kinetic energy will have been transferred into the spring in the form of potential energy. With this information in mind, we can equate the two forms of energy.
Now, we can rearrange terms in order to isolate 
.
For this question, we're told than an object is travelling with a certain velocity towards a spring. After colliding with the spring and causing it to undergo a maximum displacement, we're asked to provide an expression for the spring constant.
In order to answer this question, we'll need to consider the energy of the object and the spring during the process described. First, the object is moving with a certain velocity towards the spring. Thus, the object has kinetic energy. When the object collides with the spring and displaces the spring to its maximum displacement, there will be a brief instant where the object has completely stopped moving. At this point, all of the block's kinetic energy will have been transferred into the spring in the form of potential energy. With this information in mind, we can equate the two forms of energy.
Now, we can rearrange terms in order to isolate
A toy car is set up on a frictionless track containing a downward sloping ramp and a vertically oriented loop. Assume the ramp is tall. The car starts at the top of the ramp at rest.
What additional piece of information is necessary to calculate the maximum height of the loop if the car is to complete the loop and continue out the other side?
A toy car is set up on a frictionless track containing a downward sloping ramp and a vertically oriented loop. Assume the ramp is
What additional piece of information is necessary to calculate the maximum height of the loop if the car is to complete the loop and continue out the other side?
Tap to see back →
This is an example of conservation of energy. The car starts at the top of the ramp, at height . It has no velocity at this time since it is starting from a rest. Therefore its total energy is where is the mass of the car and is the value of gravitational acceleration.
At the bottom of the loop, all of the potential energy will have been converted into kinetic energy.
As the car traverses the loop and rises above the ground, kinetic energy will be converted back into potential energy. The shape of the loop does not matter in this case -- only the vertical distance between the ground and the car.
In the tallest possible loop, all kinetic energy at the bottom is converted to potential energy at the top. This is the maximum height the car can reach -- there is no additional energy left to continue climbing a taller loop. Therefore, the potential energy at the top of the tallest loop we can build is equal to the kinetic energy at the bottom of the loop. But we have already noted that the kinetic energy at the bottom of the loop is equal to the potential energy at the top of the ramp.
Therefore, we set . We see that and cancel, and we are left with . In other words, the tallest loop you can build is equal to the height of whatever ramp you select. In this example, the tallest loop we can build is . We do not need to know the specific values of or .
This is an example of conservation of energy. The car starts at the top of the ramp, at height
At the bottom of the loop, all of the potential energy will have been converted into kinetic energy.
As the car traverses the loop and rises above the ground, kinetic energy will be converted back into potential energy. The shape of the loop does not matter in this case -- only the vertical distance between the ground and the car.
In the tallest possible loop, all kinetic energy at the bottom is converted to potential energy at the top. This is the maximum height the car can reach -- there is no additional energy left to continue climbing a taller loop. Therefore, the potential energy at the top of the tallest loop we can build is equal to the kinetic energy at the bottom of the loop. But we have already noted that the kinetic energy at the bottom of the loop is equal to the potential energy at the top of the ramp.
Therefore, we set
An elevator is designed to hold of cargo. The designers want the elevator to be able to go from the ground floor to the top of a tall building in . What is the minimum amount of power that must be delivered to the motor at the top of the shaft? Assume no friction and that the elevator itself has a negligible weight.
An elevator is designed to hold
Tap to see back →
Power is the rate of energy transfer. To raise a object , a total of or ( is required. To find the power in Watts (), we divide the total energy required by the time over which the energy must be transferred:
Power is the rate of energy transfer. To raise a
How far can a person jump while running at and a vertical velocity of ?
How far can a person jump while running at
Tap to see back →
We know that:
and we are looking for the maximum height (vertical displacement) this person can obtain, so we aren't concerned with .
We can apply the conservation of energy:
Masses cancel, so
Solve for :
(rounded to simplify our calculations)
so let's plug in what we know
. This is our final answer.
We know that:
and we are looking for the maximum height (vertical displacement) this person can obtain, so we aren't concerned with
We can apply the conservation of energy:
Masses cancel, so
Solve for
so let's plug in what we know
If a object has a kinetic energy of right after it is launched in the air, and it has KE at its max height, what is its max height?
If a
Tap to see back →
Let's first write down the information we are given:
In order to solve this problem we must apply the conservation of energy, which states since no friction.
This means that as the project reaches its max height energy is converted from Kinetic Energy (energy of motion) to potential gravitational energy (based off of height).
We can subtract from to get the at its max height
=
so we can solve for the height
where
therefore
Let's first write down the information we are given:
In order to solve this problem we must apply the conservation of energy, which states
This means that as the project reaches its max height energy is converted from Kinetic Energy (energy of motion) to potential gravitational energy (based off of height).
We can subtract
so we can solve for the height
where
therefore
If an object has a kinetic energy of right after it is launched in the air, and it has KE at its max height of , what is the object's mass?
If an object has a kinetic energy of
Tap to see back →
Let's first write down the information we are given:
In order to solve this problem we must apply the conservation of energy, which states since no friction.
This means that as the project reaches its max height energy is converted from Kinetic energy (energy of motion) to potential gravitational energy (based off of height).
We can subtract from to get the at its max height
=
so we can solve for the mass
where
therefore
Let's first write down the information we are given:
In order to solve this problem we must apply the conservation of energy, which states
This means that as the project reaches its max height energy is converted from Kinetic energy (energy of motion) to potential gravitational energy (based off of height).
We can subtract
so we can solve for the mass
where
therefore
A baseball weighing is dropped from a second story window which is high. What is the gravitational potential energy?
A baseball weighing
Tap to see back →
Gravitational potential energy is given by the equation:
We are given all the information needed to solve for the potential energy.
Plug in known values and solve.
Recall that the units for energy are Joules. Newtons is the unit for force.
Gravitational potential energy is given by the equation:
We are given all the information needed to solve for the potential energy.
Plug in known values and solve.
Recall that the units for energy are Joules. Newtons is the unit for force.
A bowling ball is released from in the air. What is it's gravitation potential energy upon release?
A
Tap to see back →
The equation for gravitational potential energy is:
We are given all the information needed to answer the question.
Plug in known values and solve.
The equation for gravitational potential energy is:
We are given all the information needed to answer the question.
Plug in known values and solve.
A bouncy ball is dropped from . When it bounces back up is reaches a height of . How much energy was loss?
A
Tap to see back →
The formula for gravitational potential energy is:
To find the potential energy lost, we need to find the potential energy of the ball at two heights, then find the difference.
Note that the energy was not actually lost; rather, it was converted to kinetic energy.
The formula for gravitational potential energy is:
To find the potential energy lost, we need to find the potential energy of the ball at two heights, then find the difference.
Note that the energy was not actually lost; rather, it was converted to kinetic energy.
A car traveling at has a kinetic energy . If the car accelerates to , what will the new kinetic energy be?
A car traveling at
Tap to see back →
Kinetic energy is given by. We will begin by calculating the car's initial kinetic energy, in terms of the unknown mass of the car :
.
Next, we will calculate the final energy of the car, also in terms of the unknown mass of the car:
.
To find the ratio of the final to initial kinetic energy, we divide by . We see that this reduces to with the both the mass and terms cancelling. . Thus, the new kinetic energy is .
Kinetic energy is given by
Next, we will calculate the final energy of the car, also in terms of the unknown mass of the car:
To find the ratio of the final to initial kinetic energy, we divide