College Physics : Mechanics

Example Questions

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Example Question #1 : Mechanics

A car traveling at  has a kinetic energy . If the car accelerates to , what will the new kinetic energy be?

The mass of the car is required

Explanation:

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 .

Example Question #2 : Kinetic Energy

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?

Explanation:

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.

Example Question #1 : Work And Energy

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?

The exact shape of the loop

The value of

The distance between the end of the ramp and entrance to the loop

The mass of the car

None

None

Explanation:

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 .

Example Question #2 : Work And Energy

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.

Explanation:

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:

Example Question #3 : Work And Energy

How far can a person jump while running at   and a vertical velocity of   ?

Explanation:

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.

Example Question #1 : Conservation Of Momentum And Energy

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?

Explanation:

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

Example Question #1 : Conservation Of Momentum And Energy

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?

Explanation:

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

Example Question #6 : Work And Energy

bouncy ball is dropped from . When it bounces back up is reaches a height of . How much energy was loss?

Explanation:

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.

Example Question #7 : Work And Energy

A baseball weighing  is dropped from a second story window which is  high. What is the gravitational potential energy?

Explanation:

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.

Example Question #8 : Work And Energy

bowling ball is released from  in the air. What is it's gravitation potential energy upon release?