Calculating Energy

Studying energy involves determining the amount of energy an object has. This energy can be kinetic or potential, or it could be a combination of both. In this lesson, you'll practice deciding what kind of energy an object has, and you'll calculate its kinetic and potential energy. 

 

Problem Solving with Kinetic and Potential Energy

The objects in this lesson's problems will only have gravitational potential energy (GPE). They will not have elastic potential energy (EPE). There are going to be two types of problems. 

The goal in the first type of problem will be to determine if an object has GPE, kinetic energy (KE) or both. Then you will find the numerical value of each. 

The goal in the second type of problem will be to determine the height or the speed of an object, knowing its GPE or its KE. 

There are two equations you need to use on the worksheet:

 

 

 

In both equations m stands for mass and needs to be measured in kilograms (kg). The speed is shown by v, measured in meters per second (m/s). The height is h, measured in meters (m), and lastly g is the gravitational constant that has a value of 9.8 m/s². 

 

Riding the Ferris Wheel to the Top

Once the Ferris wheel is loaded and gets to traveling at top speed, Jessie wants to know how much energy she has. When at the highest point on the circle, Jessie is 30 meters off the ground. The Ferris wheel spins at 5 m/s at top speed. How much energy does Jessie, who has a mass of 50 kg, have at the highest point of the circle?

How do you solve this problem? First, gather some information.

1.   Where is the object? 30 meters above ground

2.   Is the object moving (yes or no); if yes, what is its speed? yes, 5 m/s

3.   What is the object’s mass? 50 kg

 

Now use your answers to the first three questions to complete this part.

Does the object have GPE? Remember, an object has GPE if it is some height off the ground. 

If yes, then solve using GPE = mgh

yes, it has GPE

(50 kg) (9.8 m/s²) (30 m)=14,700 joules

 

Does the object have KE? Remember, an object has KE if it is moving.

If yes, then solve using KE = ½ mv^{2 Â} 

Yes, it has KE

½ (50 kg) (5 m/s)²= 625 joules

 

Riding the Ferris Wheel to the Bottom

Once the Ferris wheel is loaded and gets to traveling at top speed, Jessie wants to know how much energy she has. When at the highest point on the circle, Jessie is 30 meters off the ground. The Ferris wheel spins at 5 m/s at top speed. How much energy does Jessie have at the lowest point of the circle?

 

Gather information.

 

Where is the object? 0 meters

Is the object moving (yes or no); if yes, at what speed?  yes, 5 m/s

What is the object’s mass? 50 kg

Now use your answers to the first three questions to complete this part.

Does the object have GPE? Remember, an object has GPE if it is some height off the ground. If yes, then solve using GPE = mgh. 

No, she doesn't have GPE, she is at ground level. Here is the math to prove it:

 

(50 kg) (9.8 m/s²) (0 m)=0 joules

 

Does the object have KE? Remember, an object has KE if it is moving. If yes, then solve using KE = ½ mv²

^ 

Yes, she has KE.

½ (50 kg) (5 m/s)²= 625 joules

 

Sitting at the Top of the Ferris Wheel

Once the Ferris wheel is loaded and gets to traveling at top speed, Jessie wants to know how much energy she has. When at the highest point on the circle, Jessie is 30 meters off the ground. The Ferris wheel spins at 5 m/s at top speed. When the ride slows down and people are let off the ride, Jessie is stuck at the top of the circle, at rest. How much energy does she have now?

 

Gather Information.

Where is the object? 30 m above ground

Is the object moving (yes or no); if yes, at what speed? No, she is at rest, so her speed is 0 m/s.

What is the object’s mass? 50 kg

 

Now use your answers to these questions to complete this part.

 

Does the object have GPE? Remember, an object has GPE if it is some height off the ground. If yes, then solve using GPE = mgh

Yes, she has GPE.

(50 kg) (9.8 m/s²) (30 m)=14,700 joules

Does the object have KE? Remember, an object has KE if it is moving. If yes, then solve using KE = ½ mv²

No, she is at rest. Here is the math to prove it:

 

½ (50 kg) (0 m/s)²= 0 joules

 

Step-by-step Problem Solving

Review is never a bad thing, especially when the review walks you through the problems step-by-step. Check out the example problem to see the Ferris wheel problem solved again.

Finding Height with GPE

Directions: View each step below in the example problem.

 

Step 1

Read the problem and find all given values. Then find the value you need to determine. Make a list of these values.

 

At one point on the Ferris wheel ride, Jessie, who has a mass of 50 kg, has 4,900 joules of GPE. How high is she off the ground?

 

Mass =50 kg

GPE = 4,900 joules

Height = ?

 

Step 2

Look at your equations and choose the appropriate one for the values you have in your problem. Once you have your equation, fill in the known values. Remember that g is a known value. It is the gravitational constant, 9.8 m/s².

 

Mass =50 kg

GPE = 4,900 joules

Height = ?

 

GPE = mgh

4900 J= (50 kg) (9.8 m/s²) h

 

Step 3

Multiply the 50 kg times the 9.8 m/s²)to simplify the equation. Now you have 4,900 joules equals 490 newtons times h. You want h, so you have to get it by itself. You do this by dividing. And now you have your answer!

 

Isolate the variable you are solving for.

 

4,900 J= (50 kg) (9.8 m/s²) h

 

(50 kg)(9.8 m/s²) = 490 N

So,

4,900 J = (490 N) x h

 

h = 4,900 J/490 N = 10 m

 

Example Problem: Finding Speed with KE

 

Directions: View each step below in the example problem.

 

Step 1

Read the problem and find all the given values. Then find the value you need to determine. Make a list of these values.

 

A ball rolls down a ramp. The ball has a mass of 1 kg and it has 18 joules of kinetic energy. What is the ball’s speed?

 

m = 1 kg

KE = 18 joules

v = ?

 

Step 2

Look at your equations and choose the appropriate one for the values you have in your problem. Once you have your equation, fill in the known values.

 

m = 1 kg

KE = 18 joules

v = ?

 

KE = ½ mv²

18 J = ½ (1 kg) v²

 

Step 3

Once you have 18 equals 0.5 v², you need to get the v² by itself. You divide the 18 by 0.5, which equals 36. Then you have to take the square root to get to v. The square root of 36 is 6. (You can use your calculator square root function to help you with this.)

 

Isolate the variable you are solving for.

 

18 J = ½ (1 kg) v²

18 = 0.5 v²

v² = 36

v = 6 m/s

 

Assignment: Kinetic Energy and Potential Energy Math Exploration

In this lesson, the goal of some problems was to determine the kinetic and potential energies of the object. Other problems asked you to calculate the height and the speed. Now it's your turn to try these on your own. Be sure to show your work where possible. 

Remember to use the equations provided and the sample problems as a guide.

 

 

 

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