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High School Physics : Calculating Potential Energy

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Example Question #51 : Energy

A 1.12kg book falls off the top of a 2.03m bookshelf. What is its potential energy right before it falls?

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

Possible Answers:

32.16J

8.92J

13.85J

22.28J

7.99J

Correct answer:

22.28J

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.

$PE=1.12kg*-9.8\frac{m}{s^2}*-2.03m$

PE=22.28J

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Example Question #52 : Energy

A 3.23kg book falls off the top of a 3.01m bookshelf. What is its potential energy right before it falls?

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

Possible Answers:

123.38J

95.28J

98.23J

31.76J

16.04J

Correct answer:

95.28J

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.

$PE=3.23kg*-9.8\frac{m}{s^2}*-3.01m$

PE=95.28J

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Example Question #53 : Energy

What is the potential energy of a 0.5kg ball held above the ground?

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

Possible Answers:

14.7J

1.63J

6.3J

We need to know the final velocity to solve

29.4J

Correct answer:

14.7J

Explanation:

The formula for gravitational potential energy is:

PE=mgh

We are given the mass of the ball, height, and acceleration from gravity. Remember, since the displacement is downward it must be negative.

$PE=0.5kg*-9.8\frac{m}{s^2}*-3m$

PE=14.7J

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Example Question #54 : Energy

A box is placed on top of a $\small 3m$ tall spring resting on the ground. The box has a weight of $\small 10N$ , and compresses the spring $\small 1m$ . What is the spring constant?

Possible Answers:

$5\frac{N}{m}$

$10\frac{N}{m}$

$40\frac{N}{m}$

$20\frac{N}{m}$

$30\frac{N}{m}$

Correct answer:

$20\frac{N}{m}$

Explanation:

We need two formulas for this problem: the gravitational potential energy and the spring potential energy.

PE_g = mgh

$PE_s = \frac{1}{2}kx^2$

We know the weight of the box and the change in height when it is placed on the spring. These values allow us to calculate the change in potential energy. Due to conservation of energy, the total energy must remain constant. Initially, the box only has gravitational potential energy. In its final position, it has both gravitational and spring potential energy.

PE_i=PE_f

$PE_{g1}=PE_{g2}+PE_s$

$mgh_1=mgh_2+\frac{1}{2}kx^2$

We know the initial height and final height of the spring. This also gives us the value of $\small x$ , the displacement of the spring.

$mg(3m)=mg(2m)+\frac{1}{2}k(1m)^2$

We also know the weight of the box: $\small mg=10N$

$(10N)(3m)=(10N)(2m)+\frac{1}{2}k(1m)^2$

Now we can solve for the spring constant, $\small k$ .

$30J=20J+\frac{1}{2}k(1m^2)$

$10J=(\frac{1}{2}m^2)k$

$20\frac{N}{m}=k$

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Example Question #55 : Energy

Calculate the potential energy of a $\small 500g$ branch attached to a tree at a point $\small 30m$ above the ground.

Possible Answers:

1530J

80J

15J

147J

163J

Correct answer:

147J

Explanation:

Potential energy due to gravity is given by the equation:

PE=mgh

We are given the mass of the branch and its height. Gravity is constant. Using these values, we can solve for the potential energy.

First, convert the mass of the branch to kilograms.

$500g*\frac{1kg}{1000g}=0.5kg$

Then, use the equation to find the energy.

$PE=(0.5kg)(9.8\frac{m}{s^2})(30m)$

PE=147J

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Example Question #56 : Energy

A man stands at the top of a 21m tall building. He holds a 3.2kg rock over the edge. What is the potential gravitational energy of the rock?

Possible Answers:

67.2J

658.56J

689.92J

77J

6.86J

Correct answer:

658.56J

Explanation:

Potential gravitational energy is given by the equation:

PE=mgh

We are told the height of the rock and its mass. Using the constant acceleration due to gravity, we can solve for the gravitational potential energy.

$PE=(3.2kg)(9.8\frac{m}{s^2})(21m)$

$PE=658.56\ \frac{kg\cdot m^2}{s^2}=658.56J$

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Example Question #51 : Energy

Sam throws a 0.5kg rock off the edge of a 10m tall building at an angle of $35^{\circ}$ from the horizontal. The rock has an initial speed of $30\frac{m}{s}$ .

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

What is the gravitational potential energy of the rock as soon as it leaves Sam's hand?

Possible Answers:

98J

49J

106J

30J

22J

Correct answer:

49J

Explanation:

The formula for gravitational potential energy is PE=mgh . The only relevant variables are mass, gravity, and height. All of the information about velocity and angle are not needed to solve for the initial potential energy.

Plug in the given values for mass and height, and solve using the equation. Keep in mind that the height will be negative because the rock travels downward.

h=y_2-y_1=0m-10m=-10m

$PE=(0.5kg)(-9.8\frac{m}{s^2})(-10m)$

PE=49J

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Example Question #58 : Energy

Laurence throws a 0.5kg rock off the edge of a 12m tall building at an angle of $20^{\circ}$ from the horizontal with an initial speed of $31\frac{m}{s}$ .

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

What is the potential energy of the rock at the moment it is released?

Possible Answers:

112.2J

106.6J

49.7J

58.8J

29.4J

Correct answer:

58.8J

Explanation:

The formula for gravitational potential energy is:

PE=mgh

We can solve for this value using the given mass of the rock, acceleration of gravity, and initial height.

$PE=(0.5kg)(9.8\frac{m}{s^2})(12m)$

PE=58.8J

This value is independent of the kinetic energy of the rock, and is not dependent on initial velocity.

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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 #51 : Energy

Example Question #52 : Energy

Example Question #53 : Energy

Example Question #54 : Energy

Example Question #55 : Energy

Example Question #56 : Energy

Example Question #51 : Energy

Example Question #58 : Energy

All High School Physics Resources

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