# High School Physics : Understanding Kinetic and Potential Energies

## Example Questions

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### Example Question #1 : Understanding Kinetic And Potential Energies

Which of the following is not an example of potential energy?

A running woman

A tightly stretched rubber band

An apple dangling off a branch

An incredibly compressed spring

A candy bar

A running woman

Explanation:

The running woman has kinetic energy as she is moving.

The candy bar has chemical potential energy.

The apple has gravitational potential energy.

The rubber band and the spring both have elastic potential energy.

### Example Question #1 : Understanding Kinetic And Potential Energies

book falls off the top of a  bookshelf. What is its kinetic energy right before it hits the ground?

Explanation:

Remember the law of conservation of energy: the total energy at the beginning equals the total energy at the end. In this case, we have only potential energy at the beginning and only kinetic energy at the end. (The initial velocity is zero, and the final height is zero).

If we can find the potential energy, we can find the kinetic energy. The formula for potential energy is .

Using our given values for the mass, height, and gravity, we can solve using multiplication. Note that the height becomes negative because the book is traveling in the downward direction.

The kinetic energy will also equal , due to conservation of energy.

### Example Question #1 : Understanding Kinetic And Potential Energies

book falls off the top of a  bookshelf. What is its kinetic energy right before it hits the ground?

Explanation:

Remember the law of conservation of energy: the total energy at the beginning equals the total energy at the end. In this case, we have only potential energy at the beginning and only kinetic energy at the end. (The initial velocity is zero, and the final height is zero).

If we can find the potential energy, we can find the kinetic energy. The formula for potential energy is .

Using our given values for the mass, height, and gravity, we can solve using multiplication. Note that the height becomes negative because the book is traveling in the downward direction.

The kinetic energy will also equal , due to conservation of energy.

### Example Question #4 : Understanding Kinetic And Potential Energies

A man stands on a tall ladder of height . He leans over a little too far and falls off the ladder. If his mass is , what is his velocity right before he hits the ground?

Explanation:

For this problem, use the law of conservation of energy. This states that the total energy before the fall will equal the total energy after the fall. The initial kinetic energy will be zero, and the final potential energy will be zero; thus, the initial non-zero potential energy will be equal to the final non-zero kinetic energy.

From there, expand the equation to include the individual formulas for potential and kinetic energy calculation.

Notice that the mass will cancel out from both sides.

Now we can solve for the final velocity in terms of the initial height.

### Example Question #1 : Understanding Kinetic And Potential Energies

A man stands on a tall ladder of height . He leans over a little too far and falls off the ladder. If his mass is , what is his potential energy right before he falls?

Explanation:

The potential energy at a given height it the product of the height, the mass of the object, and the acceleration of gravity.

Potential gravitational energy is given from the equation:

### Example Question #1 : Understanding Kinetic And Potential Energies

A ball drops from a height . What more do we need to calculate initial potential energy?

Initial velocity

Final velocity

Horizontal displacement

Elasticity of the ball

Mass

Mass

Explanation:

The formula for potential energy is:

Since  is a constant, the acceleration due to gravity on Earth, we only need the mass and the height. The problem gives a height, so we only need mass.

Given the mass and the height, we would be able to calculate the initial potential energy.

### Example Question #7 : Understanding Kinetic And Potential Energies

A runner arrives at the bottom of a hill. He runs up the hill with a constant acceleration until he reaches the top, then runs at a steady pace along the top of the hill. When are the kinetic and potential energies of this man at their greatest?

Potential energy is greatest at the top of the hill and kinetic energy is greatest at the bottom of the hill

Potential energy is greatest at the top of the hill and kinetic energy remains constant

Potential energy is greatest at the bottom of the hill and kinetic energy is greatest at the top of the hill

Potential energy is greatest at the bottom of the hill and kinetic energy is greatest at the bottom of the hill

Potential energy is greatest at the top of the hill and kinetic energy is greatest at the top of the hill

Potential energy is greatest at the top of the hill and kinetic energy is greatest at the top of the hill

Explanation:

To answer this question, we can address each type of energy separately. There is no conservation of energy in this problem; kinetic energy is not converted to potential energy as the man runs up the hill. Instead, he is accelerating, indicating an outside force that disallows conservation of energy.

First, we will find the maximum potential energy using the equation:

The man's mass and the acceleration of gravity will remain constant. The only changing variable is height. When the height is greatest, the potential energy will be the greatest. We can conclude that the potential energy will thus be greatest at the top of the hill.

Now we will look at the equation for kinetic energy:

The man's mass will remain constant, and the only changing variable will be the velocity. We are told that the man accelerates as he runs up the hill, indicating that his velocity is increasing. This tells us that he will reach a maximum velocity when he reaches the top of the hill, at which point he maintains a steady velocity along the top of the hill. Since kinetic energy is at a maximum when velocity is at a maximum, we can conclude that kinetic energy is greatest at the top of the hill.

### Example Question #1 : Understanding Kinetic And Potential Energies

A mass is put at the end of a spring with a spring constant of . The spring is then compressed . What is the maximum velocity of the mass?

Explanation:

For this problem, we're going to use the law of conservation of energy. Since we're looking for max velocity, we're going to say that the  of the system.

The formula for potential energy of a spring is

Therefore:

Notice that the 's cancel out.

Plug in our given values.

### Example Question #1 : Understanding Kinetic And Potential Energies

Sam throws a  rock off the edge of a  tall building at an angle of  from the horizontal. The rock has an initial speed of .

What is the total vertical mechanical energy as the rock leaves Sam's hand?

Explanation:

Total mechanical energy is the sum of potential energy and mechanical energy.

We can expand this equation to include the formulas for kinetic and potential energy.

Since we are only looking at vertical energies, we need to find the initial vertical velocity to apply toward the kinetic energy.

To find the vertical velocity we use the equation .

We can plug in the given values for the angle and initial velocity to solve.

Now we have all the terms necessary to solve for the total energy. Keep in mind that the change in height is going to be negative, since the rock is traveling downward.

### Example Question #1 : Understanding Kinetic And Potential Energies

Laurence throws a  rock off the edge of a  tall building at an angle of  from the horizontal with an initial speed of .

.

What is the total mechanical energy in the vertical direction when the rock is released?