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High School Physics : Calculating Potential Energy

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Example Question #1 : Calculating Potential Energy

A skier is at the top of a hill. At the bottom of the hill, she has a velocity of $\small 12\frac{m}{s}$ . How tall was the hill?

Possible Answers:

7.35 m

7.22 m

8.12 m

0.735 m

0.832 m

Correct answer:

7.35 m

Explanation:

At the top of the hill the skier has purely potential energy. At the bottom, she has purely kinetic energy.

We can solve by understanding the conservation of energy. The skier's energy at the top of the hill will be equal to her energy at the bottom of the hill.

$PE_{top}=KE_{bottom}$

Using the equations for potential and kinetic energy, we can solve for the height of the hill.

$mgh=\frac{1}{2}mv^2$

The masses cancel, and we can plug in our final velocity and gravitational acceleration.

$gh=\frac{1}{2}v^2$

$(-9.8\frac{m}{s^2})h=\frac{1}{2}(12\frac{m}{s})^2$

$(-9.8\frac{m}{s^2})h=\frac{1}{2}144\frac{m^2}{s^2}$

$(-9.8\frac{m}{s^2})h=72\frac{m^2}{s^2}$

$h=\frac{72\frac{m^2}{s^2}}{-9.8\frac{m}{s^2}}$

h=-7.35m

This formula solves for the change in height. The negative sign implies she travelled in a downward direction. Because the question is asking how tall the hill is, we use an absolute value.

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Example Question #2 : Calculating Potential Energy

An astronaut is on a new planet. She discovers that if she drops a space rock from 10m above the ground, it has a final velocity of $3\frac{m}{s}$ just before it strikes the planet surface. What is the acceleration due to gravity on the planet?

Possible Answers:

$-8.88\frac{m}{s^2}$

$0.12\frac{m}{s^2}$

$-9.8\frac{m}{s^2}$

$-1.33\frac{m}{s^2}$

$-0.45\frac{m}{s^2}$

Correct answer:

$-0.45\frac{m}{s^2}$

Explanation:

We can use conservation of energy to solve. The potential energy when the astronaut is holding the rock will be equal to the kinetic energy just before it strikes the surface.

PE=KE

$mgh=\frac{1}{2}mv^2$

Now, we need to solve for $\small g$ , the gravity on the new planet. The masses will cancel out.

$gh=\frac{1}{2}v^2$

Plug in the given values and solve.

$g(-10m)=\frac{1}{2}(3\frac{m}{s})^2$

$g(-10m)=\frac{1}{2}(9\frac{m^2}{s^2})$

$g(-10m)=(4.5\frac{m^2}{s^2})$

$g=\frac{4.5\frac{m^2}{s^2}}{-10m}$

$g=-0.45\frac{m}{s^2}$

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Example Question #1 : Calculating Potential Energy

A 0.5kg ball is about to roll off the edge of a 1.5m tall table. What is its current potential energy?

$\small g=-9.8\frac{m}{s^2}$

Possible Answers:

13.33J

14.7J

3.72J

7.35 J

9.87J

Correct answer:

7.35 J

Explanation:

The equation for potential energy is PE=mgh . We are given the mass of the ball, the height of the table, and the acceleration of gravity in the question. The distance the ball travels is in the downward direction, making it negative.

Plug in the values, and solve for the potential energy.

$PE=(0.5kg)(-9.8\frac{m}{s^2})(-1.5m)$

PE=7.35J

The units for energy are Joules.

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Example Question #4 : Calculating Potential Energy

A pendulum with string length 1.2m is dropped from rest. If the mass at the end of the pendulum is 2.03kg , what is its initial potential energy?

$\small g=-9.8\frac{m}{s^2}$

Possible Answers:

46.12J

14.42J

12.32J

23.87J

18.87J

Correct answer:

23.87J

Explanation:

Potential energy can be found using the equation PE=mgh . For the pendulum, the height is going to be the length of the string.

Remember, your height is your change in distance. In this case the ball will go down 1.2m , so the height will be negative since the ball travels downward.

$PE= (2.03kg)(-9.8\frac{m}{s^2})(-1.2m)$

PE=23.87J

The units for energy are Joules.

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Example Question #1 : Calculating Potential Energy

A 0.5kg ball rolls up a hill. If the ball is initially travelling with a velocity of $3.12\frac{m}{s}$ , how high up the hill does it roll?

$\small g=-9.8\frac{m}{s^2}$

Possible Answers:

0.52m

9.8m

0.48 m

0.03m

0.50m

Correct answer:

0.50m

Explanation:

Use the conservation of energy equation to solve for the potential energy at the top of the hill.

$PE_{top}=KE_{bottom}$

$mgh=\frac{1}{2}mv^2$

Plug in the values given to you and solve for the final height.

$(0.5kg)(9.8\frac{m}{s^2})(h)=\frac{1}{2}(0.5kg)(3.12\frac{m}{s})^2$

$4.9\frac{kg\cdot m}{s^2}h=2.4336\frac{kg\cdot m^2}{s^2}$

$h=\frac{2.4336\frac{kg\cdot m^2}{s^2}}{4.9\frac{kg\cdot m}{s^2}}$

$h=0.497m\approx0.5m$

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Example Question #1 : Calculating Potential Energy

Rob throws a ball vertically in the air with an initial velocity of $3.5\frac{m}{s}$ . What is the maximum height of the ball?

$\small g=-9.8\frac{m}{s^2}$

Possible Answers:

1.22m

0.87m

0.71m

0.32m

0.63m

Correct answer:

0.63m

Explanation:

The maximum height will be when the ball has only potential energy, and no kinetic energy. Initially, the ball has only kinetic energy and no potential energy. We can set these values equal to each other due to conservation of energy.

$PE_{top}=KE_{bottom}$

$mgh=\frac{1}{2}mv^2$

The masses will cancel out.

$gh=\frac{1}{2}v^2$

Plug in the values that were given and solve for the height.

$(9.8\frac{m}{s^2})h=\frac{1}{2}(3.5\frac{m}{s})^2$

$(9.8\frac{m}{s^2})h=\frac{1}{2}(12.25\frac{m^2}{s^2})$

$(9.8\frac{m}{s^2})h=6.125\frac{m^2}{s^2}$

$h=\frac{6.125\frac{m^2}{s^2}}{9.8\frac{m}{s^2}}$

h=0.625m

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Example Question #1 : Calculating Potential Energy

A 1.11kg ball sits at rest on a table 1.72m above the ground. What is the potential energy of the ball?

$\small g=-9.8\frac{m}{s^2}$

Possible Answers:

37.42J

31.2J

9.36J

18.71J

4.32J

Correct answer:

18.71J

Explanation:

The only potential energy this ball can have is gravitational potential energy. The formula for gravitational potential energy is PE=mgh .

We are given the height and mass of the ball. Using the given values, we can solve for the potential energy.

Keep in mind that the displacement will be negative because the ball is traveling in the downward direction.

$PE=(1.11kg)(-9.8\frac{m}{s^2})(-1.72m)$

PE=18.71J

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Example Question #1 : Calculating Potential Energy

Two balls, one with mass 2kg and one with mass 4kg , are dropped from 30m above the ground. What is the potential energy of the 2kg ball right before it starts to fall?

$\small g=-9.8\frac{m}{s^2}$

Possible Answers:

1176J

98J

294J

147J

588J

Correct answer:

588J

Explanation:

The equation for potential energy is PE=mgh .

Since we know the mass, height, and acceleration from gravity, we can simply multiply to find the potential energy.

$PE=(2kg)(-9.8\frac{m}{s^2})(-30m)$

Note that we plugged in -30m for because the ball will be moving downward; the change in height is negative as the ball drops.

PE=588J

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Example Question #9 : Calculating Potential Energy

Two balls, one with mass 2kg and one with mass 4kg , are dropped from 30m above the ground. What is the potential energy of the 4kg ball right before it starts to fall?

$\small g=-9.8\frac{m}{s^2}$

Possible Answers:

73.5J

294J

1176J

1123J

588J

Correct answer:

1176J

Explanation:

The equation for potential energy is PE=mgh .

Since we know the mass, height, and acceleration from gravity, we can simply multiply to find the potential energy.

$PE=(4kg)(-9.8\frac{m}{s^2})(-30m)$

Note that we plugged in -30m for because the ball will be moving downward; the change in height is negative as the ball drops.

PE=1176J

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Example Question #1 : Calculating Potential Energy

A 2kg book falls off the top of a 2.3m bookshelf. What is its potential energy right before it falls?

$\small g=-9.8\frac{m}{s^2}$

Possible Answers:

450.8J

4.51J

0.47J

2.94J

45.08J

Correct answer:

45.08J

Explanation:

The formula for potential energy is PE=mgh .

Given the values for the mass, height, and gravity, we can solve using multiplication. Note that the height is negative because the book falls in the downward direction.

$PE=2kg*-9.8\frac{m}{s^2}*-2.3m$

PE=45.08J

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High School Physics : Calculating Potential Energy

Study concepts, example questions & explanations for High School Physics

All High School Physics Resources

Example Questions

Example Question #1 : Calculating Potential Energy

Example Question #2 : Calculating Potential Energy

Example Question #1 : Calculating Potential Energy

Example Question #4 : Calculating Potential Energy

Example Question #1 : Calculating Potential Energy

Example Question #1 : Calculating Potential Energy

Example Question #1 : Calculating Potential Energy

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Example Question #1 : Calculating Potential Energy

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