Work and Energy: When we don't give you what you think you need

Energy:Work Story Problems, and Law of Conservation of Energy Story Problems
Sometimes it seems like we don't give you the information you need!

Work and Energy - They're Equivalent!

When you do work, energy is transferred - the numbers match!

When you are solving problems, keep in mind that the amount of work done and the amount of energy transferred (or transformed) match each other!

Elevation Problems

Solving for WORK when given F and D

Sometimes solving for work when an object is raised is easy! The problem tells you how much force was applied (or the weight of the object) and how far it was lifted. You've done these problems before!
You try it on the next page!

Multiple Choice

How much work do you do when you lift a 30 N object 5 m?

This question could also be worded like this, since we assume you push up "as much as the object is heavy." How much work do you do when you raise an object 5 m using 30 N of force?

• 6 J

• 150 J

• 0.167 J

• 1470 J

But sometimes you have to remember that the work done is equal to the change in GPE! WORK DONE = GPE

Since the WORK done is equivalent to the change in GPE, I can ask you to solve for work, but give you what you need to solve for GPE!!!


This type of problem might look something like this: How much work does it take to put a 23 kg object on a 2.5 m shelf?

Notice that I didn't give you the F and the d (W = Fd) ... I gave you the m and the h you need to solve for the equivalent GPE (GPE = mgh). Try it on the next page!

Multiple Choice

How much work does it take to put a 23 kg object on a 2.5 m shelf?

(Remember, you're solving this using the GPE equation, not the W equation!)

• 71,875 J

• 57.5 J

• 563.5 J

• 9.2 J

It works backwards, too!

Likewise, I could ask you to solve for GPE, but give you the information you need to solve for the equivalent WORK.

Such a problem might look like this... What is the GPE of a 35 N object that has been put on a 3 m shelf? It also might look like this... It takes 35 N of force to put an object on a 3 m shelf. How much GPE does it have?

You try it on the next page!

Multiple Choice

What is the GPE of a 35 N object on a 3 m shelf?

• 157.5 J

• 11.7 J

• 1029 J

• 105 J

Horizontal Problems (X-Plane)

Kinetic energy transferred = Work Done

Work and energy are also equivalent in the X-Plane (side to side). When one object collides into another object and transfers KE into it, it is doing WORK on it. The amount of KE transferred and the amount of WORK done are the same. NOTE: This DOES NOT mean the two objects will go the same speed!

In other words, I could give you a problem where I ask you to solve for how much WORK was done, but give you the information to solve for how much KE was transferred.

Such a problem might look like this:

How much work do you do when you push a 65 kg box so that it will go 1.6 m/s?

Why don't you try to solve this on the next page!

Multiple Choice

How much work do you do when you push a 65 kg box so that it will go 1.6 m/s?

• 83.2 J

• 104 J

• 10192 J

• 166.4 J

Or it might look like this...

How much KE will an object have after you push it with 24 N of force for 6 m?

Try it!

Multiple Choice

How much KE will an object have after you push it

with 24 N of force for 6 m?

• 144 J

• 432 J

• 1411.2 J

• 864 J

Law of Conservation of Energy

Sometimes WORK doesn't have anything to do with it!

Sometimes these problems are instead about the transformation of GPE into KE, and KE into GPE. Remember our skatepark example?

​Let's say that this girl has 100 J of GPE at the top of the hill...

​At this point she has maximum velocity and minimum height (through which she could fall), so she now has 0 J of GPE, but 100 J of KE.

​Halfway down the hill, half of the GPE has turned into KE, so she has 50 J of each!

​Think of all the questions I can ask you!

I can tell you how much GPE an elevated object has, and ask you how much KE it will have RIGHT before it hits the ground (at the moment when all of the GPE has turned into KE).

I can tell you how much KE an object has RIGHT before it hits the ground, and ask how how much GPE it had before it fell.

Try one...

Multiple Choice

A book fell off a shelf. It had 60 J of KE right before it hit the ground. How much GPE did it have while it was still on the shelf?

• 588 J

• 60 J

• 6.1 J

• 0.16 J

​TOO EASY!!!!!!

Let's try a harder one... these are going to force you to think about BOTH the KE and the GPE equations!

​Think of a way to solve this problem, remembering that you'll need to use BOTH equations!

A 34 kg rock has fallen off a cliff. It is going 16.2 m/s right before it hits the ground. How high was the cliff?


Okay, think it through. Which equation will you use to find "h"?
So, what will you need to find BEFORE you can use that equation?
What equation will you have to use to accomplish that?

You try it!

Multiple Choice

A 34 kg rock has fallen off a cliff. It is going 16.2 m/s right before it hits the ground. How high was the cliff?

• 4461.48 m

• 131.22 m

• 23.5 m

• 13.4 m

Let's Try Some More!

Multiple Choice

You raise a 35 kg object to a height of 5 m. How much work did you do?

• 175 J

• 1715 J

• 7 J

• 437.5 J

Multiple Choice

You give a 200 kg object a shove, so that it leaves your hand going 3 m/s. How much work did you do when you pushed it?

• 600 J

• 900 J

• 66.7 J

• 1800 J

Multiple Choice

If you do 3555 J of work to raise an 34 kg object to 3 m; are you on Earth?

• Yes

• No, you are on a less massive planet.

• No, you are on a more massive planet.

Multiple Choice

A ball has 400 J of GPE before I drop it. Halfway to the ground, how much KE will it have?

• 400 J

• 200 J

• 0 J

Multiple Choice

A ball has 400 J of GPE before I drop it. Halfway to the ground, how much GPE will it still have?

• 400 J

• 200 J

• 0 J

Multiple Choice

A ball has 400 J of GPE before I drop it from 10 m. When it is 2.5 m above the ground, how much KE will it have?

• 400 J

• 200 J

• 300 J

• 100 J

Multiple Choice

A 100 kg high diver hits the water with 980 Joules of KE and no gravitational potential energy. How much GPE did it have before he dove?

• 100 J

• 980 J

• 9800 J

• 98 J

Multiple Choice

An 45 kg rock has fallen off a cliff. It is going 35 m/s right before it hits the ground. How much GPE did it have before it fell?

• 27562.5 J

• 55125 J

• 62.5 J

• 125 J

Multiple Choice

A 100 kg high diver hits the water with 980 Joules of kinetic energy and no gravitational potential energy. If the diver started from rest on the diving platform, from what height did the diver fall?

• 0.1 meters

• 1 meter

• 10 meters

• 100 meters

Multiple Choice

A 23 kg object falls. Right before it hits the ground, it is going 14 m/s. How high did it fall from?

• 8.5 meters
• 230 meters

• 2254 meters

• 10 meters