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Lesson 3 Gravitational and Kinetic Energy Calculations

  Virtual Lab

Potential Energy on Shelves © 2017 Explore Learning 
Work through this activity to discover how gravity gives objects potential energy because of their position above the floor.

Remember that potential energy is the energy an object has because of its position or shape.

Please note: if you scroll down while in the Gizmo you will see a list of questions. You DO NOT need to complete these questions. You are able to complete them for extra practice if you would like.




  1. Click on the play button to open the activity. This activity can also be accessed in the Online Resources for Print Students section of your online course.
  2. Which object on the “SIMULATION” pane has the least potential energy? Why?

    The ball most likely has the least potential energy because it is sitting at ground level.
  1. Click on the “TABLE” tab. The potential energy (Ep) of each object is given in joules (J).

    List the objects in order from lowest to highest potential energies.

    Ball, paper, clips
Activity A:
Factors Affecting Ep
Get the Gizmo ready:
  • Select the “BAR CHART” tab and turn on “Show numerical values.”
C3.3 Image of bar chart
What factors affect how much gravitational potential energy an object has?

  1. Which of the following factors do you think affect an object’s potential energy: mass, vertical position, velocity, horizontal position?

    mass and vertical position

  1. Drag the ball to the 1 m shelf on the “SIMULATION” pane.
    What is the ball’s potential energy (Ep)?

    Move the ball to the 2 m shelf. What is its potential energy now?

    What do you think the ball’s potential energy will be on the 3 m shelf?

    The 4 m shelf?

    Use the Gizmo to check your answers. (Click the  control on the bar graph to zoom out.)


  2. Move the ball from side to side (left to right) while trying to keep it at the same height.
    How does changing the horizontal position of the ball affect its potential energy?


    Changing the ball’s horizontal position does not affect its potential energy.
  3. Place the ball and the paper on the same shelf.
    Which object has more potential energy?

    The ball
    Why do you think their potential energies are different?

    Your answer will be a variation of the following. The ball has more mass than the paper.
    Activity B:
    Calculating Ep
    		Get the Gizmo ready:
    • You will need a calculator to complete this activity.
    C3.4 Image of various objects
    Use the gravitational potential energy equation to determine the weight, mass, and potential energy of various objects.
    Ep = weight (W) x height heart

  4. Position all three objects on the 1 m shelf and fill in the third column of the table.

    Object Height (m)
    		Ep (J or N•m) 
    		Weight (N)
    Ball 1

    Clips 1

    Paper 1


    Object Height (m)
    		Ep (J or N•m)
    		Weight (N)
    Ball 1
    		 0.98
    		 0.98
    Clips 1
    		 0.39
    		 0.39
    Paper 1
    		 0.08
    		 0.08

  5. For each object, substitute the values you know into the gravitational potential energy equation to solve for weight. Record each object’s weight in the fourth column.

    For example, to calculate the weight of the ball:

    Ep = weight (W) x height (h)

    To isolate weight, you must divide each side by height. To move h to the other side, you need to use the opposite operation.

      «math» «mfrac» «msub» «mi»E«/mi» «mi»p«/mi» «/msub» «mi»h«/mi» «/mfrac» «mo»=«/mo» «mfrac» «mrow» «mi»W«/mi» «mi»h«/mi» «/mrow» «mi»h«/mi» «/mfrac» «/math»

    Now, cancel the like terms.

    «math» «mfrac» «msub» «mi»E«/mi» «mi»p«/mi» «/msub» «mi»h«/mi» «/mfrac» «mo»=«/mo» «mi»W«/mi» «mspace linebreak=¨newline¨»«/mspace» «mi»W«/mi» «mo»=«/mo» «mfrac» «msub» «mi»E«/mi» «mi»p«/mi» «/msub» «mi»h«/mi» «/mfrac» «mspace linebreak=¨newline¨»«/mspace» «mi»W«/mi» «mo»=«/mo» «mfrac» «mrow» «mn»0«/mn» «mo».«/mo» «mn»98«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»J«/mi» «/mrow» «mrow» «mn»1«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «/mrow» «/mfrac» «mspace linebreak=¨newline¨»«/mspace» «mi»W«/mi» «mo»=«/mo» «mn»0«/mn» «mo».«/mo» «mn»98«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»N«/mi» «/math»



  1. Suppose the clips were placed on the 5 m shelf. What would their gravitational potential energy be? (Show your work.)

    Ep = Wh
    Ep = (0.39 N)(5 m)
    Ep = 1.95 J or N•m 

    Use the Gizmo to check your answer.


    The Gizmo gives a value of 1.96 J.



    Activity C:
    Work and Ep
    		Get the Gizmo ready:
    • Place the ball, clips, and paper at 0 m.
    C3.5 image of various objects
    How much work is done to lift the ball, clips, and paper?

  2. How much potential energy do the ball, clips, and paper have now?

  3. Use the weight of the ball that you calculated in activity B to determine how much work would be required to lift the ball 2 metres above the zero position.

    W = Fd
    W = (0.98 N)(2 m)
    W = 1.96 J or N•m
  4. Move the ball to the 2 m shelf.

    How much potential energy does the ball have now?

    How does the ball’s potential energy relate to the amount of work needed to place the ball on the 2 m shelf?

    The two values are equal.
    How much work would be needed to lift the ball from the 2 m shelf to the 5 m shelf and how much potential energy would it have on the 5 m shelf?

    «math»«mi»W«/mi»«mo»=«/mo»«mi»F«/mi»«mi»d«/mi»«mspace linebreak=¨newline¨»«/mspace»«mi»W«/mi»«mo»=«/mo»«mfenced»«mrow»«mn»0«/mn»«mo».«/mo»«mn»98«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»N«/mi»«/mrow»«/mfenced»«mfenced»«mrow»«mn»5«/mn»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»m«/mi»«/mrow»«/mfenced»«mspace linebreak=¨newline¨»«/mspace»«mi»W«/mi»«mo»=«/mo»«mn»2«/mn»«mo».«/mo»«mn»94«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»J«/mi»«mo»§#160;«/mo»«mi»or«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»N«/mi»«mo»§#183;«/mo»«mi mathvariant=¨normal¨»m«/mi»«mspace linebreak=¨newline¨»«/mspace»«msub»«mi»E«/mi»«mi»p«/mi»«/msub»«mo»=«/mo»«mi»W«/mi»«mi»h«/mi»«mspace linebreak=¨newline¨»«/mspace»«msub»«mi»E«/mi»«mi»p«/mi»«/msub»«mo»=«/mo»«mfenced»«mrow»«mn»0«/mn»«mo».«/mo»«mn»98«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»N«/mi»«/mrow»«/mfenced»«mfenced»«mrow»«mn»5«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»m«/mi»«/mrow»«/mfenced»«mspace linebreak=¨newline¨»«/mspace»«msub»«mi»E«/mi»«mi»p«/mi»«/msub»«mo»=«/mo»«mn»4«/mn»«mo».«/mo»«mn»90«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»J«/mi»«/math»
  5. Please return to the top of this page and click on analysis to complete the analysis questions.
  1. What is the relationship between an object’s height above the ground and its gravitational potential energy?

    As an object’s height increases, so does its potential energy.

  2. What two factors affect how much gravitational potential energy an object has?

    Height above the ground and mass.

  3. What is the gravitational potential energy of a 4 000 kg elephant hoisted 20 m above the earth's surface?

    Step 1: List the variables.

    «math»«msub»«mi»E«/mi»«mi»p«/mi»«/msub»«mo»=«/mo»«mo»?«/mo»«mspace linebreak=¨newline¨»«/mspace»«mi»m«/mi»«mo»=«/mo»«mn»4«/mn»«mo»§#160;«/mo»«mn»000«/mn»«mo»§#160;«/mo»«mi»kg«/mi»«mspace linebreak=¨newline¨»«/mspace»«mi»g«/mi»«mo»=«/mo»«mn»9«/mn»«mo».«/mo»«mn»81«/mn»«mfrac»«mi mathvariant=¨normal¨»m«/mi»«msup»«mi mathvariant=¨normal¨»s«/mi»«mn»2«/mn»«/msup»«/mfrac»«mspace linebreak=¨newline¨»«/mspace»«mi»h«/mi»«mo»=«/mo»«mn»20«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»m«/mi»«/math»
    Step 2: Identify the correct formula and rearrange if necessary.

    Ep = mgh
    Step 3: Substitute the values into the formula.

    «math»«msub»«mi»E«/mi»«mi»p«/mi»«/msub»«mo»=«/mo»«mfenced»«mrow»«mn»4«/mn»«mo»§#160;«/mo»«mn»000«/mn»«mo»§#160;«/mo»«mi»kg«/mi»«/mrow»«/mfenced»«mfenced»«mrow»«mn»9«/mn»«mo».«/mo»«mn»81«/mn»«mfrac»«mi mathvariant=¨normal¨»m«/mi»«msup»«mi mathvariant=¨normal¨»s«/mi»«mn»2«/mn»«/msup»«/mfrac»«/mrow»«/mfenced»«mfenced»«mrow»«mn»20«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»m«/mi»«/mrow»«/mfenced»«/math»
    Step 4: Calculate the answer.

    Ep = 784 800 J

    The answer must be rounded to two significant digits.

    784 800 J cannot be rounded to two significant digits, so it must be put into scientific notation.
    Move the decimal point to the left until your answer is between 1 and 10.
    784 800: Move the decimal five places to the left to become 7.848 00.
    Five decimals to the left is indicated by a «math» «msup mathcolor=¨#FFFFFF¨» «mn mathcolor=¨#FFFFFF¨»10«/mn» «mn»5«/mn» «/msup» «/math» (“«math» «mn mathcolor=¨#FFFFFF¨»5«/mn» «/math»” for moving five places to the left).
    Round the value of 7.848 00 to two significant digits: 7.8.

    The gravitational potential energy of the elephant is 7.8 × 105 J.


  4. Objects in motion have kinetic energy. As objects fall, their potential energy is converted into kinetic energy. How much kinetic energy do you think the ball would have just before it hit the floor if it were dropped from a 2 m shelf? Explain your answer.

    The ball would have 1.96 J of kinetic energy because by the time the ball reached the floor, all of its potential energy would have been converted to kinetic energy.