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3.13.6

Question 110 pts
A 319 kg motorcycle is parked in a parking garage. If the car has 35,494 J of potential energy, how many meters above ground is the car? Report your answer to 1 decimal place. Please do not include units or the answer will be marked incorrect.


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Question 210 pts
A box sitting on the top of a hill has 252 J of potential energy. If the hill is 279 meters above ground, what is the box’s mass? Report your answer to two decimal places. Please do not include units or the answer will be marked incorrect.


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Question 310 pts
How much potential energy does a 7.4 kg object gain when it is lifted a distance of 1.4 meters? Report your answer to the nearest whole number. Please do not include units or the answer will be marked incorrect.


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Question 410 pts
A 30.5 kg cart has a velocity of 5 m/s. How much kinetic energy does the object have? Report your answer to 1 decimal place. Please do not include units or the answer will be marked incorrect.



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Question 510 pts
How fast is a 55.2 kg lion moving if it has 2,641 joules of energy? Please report your answer to 1 decimal place. Please do not include units or the answer will be marked incorrect.


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Question 610 pts
Object A has a mass of m with a speed of v. Object B has a mass of m and a velocity of 2v. Compared to the kinetic energy of Object A, the kinetic energy of Object B is

Group of answer choices

1/4 as large

4 times larger

1/2 as large

2 times larger

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Question 710 pts
If the speed of an object doubles and its mass is halved, how does the kinetic energy change?
Group of answer choices

It is halved

It is multiplied by 4

It doubles

It is multiplied by 1/4

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Question 830 pts
A 100 kg roller coaster is at the peak of the first hill 75 m above ground. A second later it is at the bottom of the hill.
a. Create an LOL chart for the following situation. Ignore friction and energy loss.
b. How fast was the roller coaster moving?
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Potential and Kinetic Energies
In the previous lesson, we looked at how work and energy are related. In this lesson, we will look at two of the most common forms of mechanical energy.
Potential Energy
One type of energy that we encounter is known as potential energy. Potential energy is the energy of an object or system that is based on the location or position of the object. Remember, energy is the ability of the object to do work. So potential energy means that the object could potentially use its current position to do work. For instance, an object on top of a three story building could do work if it fell to the ground. The work done would be the force exerted on the object by gravity times the distance the object fell. An object with potential energy does not need to be moving or doing work. It only has the potential to do work at some point in the future.
For the purposes of this course, we will look at two different forms of mechanical potential energy; gravitational potential energy and elastic potential energy. Elastic potential energy will be covered in the next lesson, so we will just discuss gravitational potential energy here.

Image from Wikipedia: http://upload.wikimedia.org/wikipedia/commons/b/be/Gravitational_field_Earth_lines_equipotentials.svg
Gravitational Potential Energy (GPE)
Gravitational potential energy is the energy an object has because of its position inside of a gravitational field. Since gravity always tries to move the object toward the center of the field, we will assume the field points directly downward. An object's gravitational potential energy is based on how far off the ground the object is.
The height of the object is actually a relative height based off of a reference point. In most instances, the reference point will be the ground. Changing the reference point will change the amount of potential energy that the object has, even though the position of the object hasn’t actually moved. For this reason, we often do not look at the potential energy at a specific location, but how the potential energy changes as the position of the object changes. Let’s look at how to define potential energy based on our definition of work.
We know that work is force times distance.
W = f * d
Potential energy is the ability of a stationary object to do work so the force in the work equation is the force of gravity. The distance in the equation is equal to the height of the object (h) Recall, Fw = mass times the force of gravity or Fw = m * g. Combing these equations we get:
W = m * g * h
Since potential energy (PE) is the ability to do work, we can write:
PE = m * g * h
Since the reference height is something we choose, potential energy is relative to the object’s position. If our reference point for a book on a desk is the ground, then the book has the potential to fall down. The book has positive potential energy because the object could do work by falling to the ground.
If our reference point was the top of the desk, then the object would not have any potential energy, because it was already at the reference point. If we chose the reference height as the ceiling of the room, our book would have negative potential energy. Since the book cannot fall up to the reference height by itself, energy would be needed to do work just to get it to the ceiling.

Example Problem 1
A 1 kg book sits on a desk 1.5 m above the floor. How much potential energy does the book have?
GPE = m * g * h
GPE = 1 kg * 9.8 m/s2 * 1.5 m = 29.4 J

Example Problem 2
A man carries a box on the top of his head. If the box has 150 J of potential energy and is 2.5 m above ground, what is the box’s mass?
GPE = mgh
150 = m * 9.8 * 2.5
m = 6.1 kg

Kinetic Energy
Kinetic energy is an extremely important form of mechanical energy because it has to do with the motion of an object. Unlike gravitational potential energy, kinetic energy is based on how fast an object is moving. The formula for calculating the kinetic energy that an object has is:
KE = .5 * m * v2
Notice that the speed of the object is squared. That means as an object moves faster, the kinetic energy of the object increases very quickly. Remember, we noted that energy was the "currency" that we spend to do work. An object that has kinetic energy can use that energy to accomplish something. The faster an object goes, the more work it can do as it transforms that energy into another form. We will talk more about these transformations below.

Example Problem 3
An 1800 kg car is traveling at 20 m/s. What is the car's kinetic energy?
KE = .5 * m * v2
KE = .5 * 1800 kg * (20)2
KE = 360,000 J
When the amount of joules gets into the thousands, we convert the joules to kilojoules by dividing the joules by 1000.
Here, the KE = 360 kilojoules.
Example Problem 4
How fast is a 35 kg jaguar moving if it has 1800 joules of energy?
KE = .5 * m * v2
KE/.5*m = v2
v2 =1800/(.5)(35) = 102.9
v = 10.1 m/s

The Kinetic Potential Energy Connection
In middle school you probably learned that energy can be converted from one form to another. For instance, light energy from the sun is converted to chemical energy by plants. We eat the plants and convert the chemical energy from the plant into mechanical energy that makes our body move.
Potential energy can become kinetic energy when an object begins moving. For instance, imagine a 700 kg car is resting at the top of a 100 m hill. If the car begins rolling down the hill, some of the potential energy is converted to kinetic energy. When the car reaches the bottom of the hill, all of the potential energy has been converted to kinetic energy. We can represent these conversions using charts referred to as LOL charts.

LOL Charts
The LOL chart is broken into two sections. The first chart represents the energy at the start. In this case the chart shows a bar that is all potential energy. Since this is a qualitative representation, we are not worried about numbers.
The second chart represents the energy at the end. This is when the car reaches the bottom of the hill. We will discuss the circle in the LOL chart in a later lesson. Since all of the potential energy becomes kinetic energy, the KE bar should be the same heith as the PE bar.
The LOL chart is an excellent representation of the change from potential to kinetic energy. It also helps us solve problems. Since energy is not lost just converted, we know that the the amount of potential energy at the start is equal to the amount of kinetic energy at the end. This means for this situation we can say that GPE = KE. Using the equations for GPE and KE we can write:
m * g * h = .5 * m * v2
Using the numbers from above we can find out how fast the car was moving.
700 kg * 9.8 m/s2 * 100 m = .5 * 700 kg * v2
1960 = v2
v = 44.3 m/s
The car is traveling at 44.4 m/s.

Answer 1