After his famous experiment of dropping cannon balls from the Tower of Pisa, Galileo was determined to fully describe the physical laws of falling bodies. However, freefall happened too quickly to be accurately measured using available methods, which could be as crude as counting heartbeats.

Galileo realized that he could slow down the motion of falling bodies by sliding or rolling them down an inclined plane. The discoveries that resulted from these experiments form the underpinnings of our understanding of force, acceleration, energy and gravitation.

Frictionless Sliding

Potential energy (PE) is the energy an object has due to its position or the configuration of its parts. Kinetic energy (KE) is the energy an object has due to its motion. In this activity, you will investigate how these energies change as an object slides down an inclined plane.

  1. First you will look at a single block sliding down a frictionless ramp. For Ramp 1 be sure that a Steel block will slide on a Frictionless ramp with an Angle of 20°. (To quickly set a slider to a particular value, type the value in the field to the right of the slider and press Enter.) For Ramp 2, No block should be selected.
    1. Select the ENERGY tab, and notice the black bar representing the potential energy of the block. Click Play (play button). Describe how the potential and kinetic energy change as the block slides down the ramp.
    2. Select the GRAPH tab, which should show a graph of Energy vs. Time. This graph shows the total energy of the block as it slides down the plane. Is any energy lost as potential energy is converted to kinetic energy? Explain how you can tell.
  2. Click Reset (reset button). On the CONTROLS tab, change the object on Ramp 2 to a Steel block on a Frictionless ramp with an Angle of 60°.
    1. On the GRAPH tab, select a graph of Potential energy vs. Time. Press Play and observe the potential energy curve for each ramp. How are the two curves similar? How are they different?
    2. Based on the graphs, approximately how much potential energy did each block have at the beginning of the experiment? How much at the end?
    3. Did the ramp angle affect the potential energy the blocks had at the beginning or end of the experiment?
    4. In the situation shown in this Gizmo, the formula for potential energy (in Joules) is PE = mgh, where m is the mass of the block (1 kg), g is the acceleration due to gravity (9.8 m/s2), and h is the height of the block (each ramp is 1 m high). How does this explain your above answers?
  3. Change the graph to Kinetic energy vs. Time.
    1. How much kinetic energy did each block have at the beginning of the experiment?
    2. Approximately how much kinetic energy did each block have at the end?
    3. How do these answers compare to the potential energies of the blocks at the beginning and end?
    4. The formula for kinetic energy is

      Kinetic energy

      where m is the mass of the block and v is the velocity of the block. Solve this formula for the velocity (v).
    5. Calculate the velocity of each block at the bottom of the ramp. (Recall that the mass of each block is 1 kg.)
    6. Change the graph to Velocity vs. Time to check your answers. (You can see the exact final velocity of the block on ramp 1 by selecting the TABLE tab and scrolling to the bottom.)
    7. Did the final velocity depend on the ramp angle? Explain why or why not.
    8. Run several more experiments on the frictionless ramp with different ramp angles. Did the final velocity ever change? Based on what you have discovered about potential and kinetic energy, explain why the ramp angle does not affect the final velocity of the block.
  4. Click Reset. On the SIMULATION pane, drag the block on Ramp 1 so that it is halfway down the ramp.
    1. Calculate how much potential energy this block had at the beginning of the experiment, when it was halfway up the ramp.
    2. How much kinetic energy does the block have at the bottom of the ramp?
    3. Calculate the velocity the block will have at the bottom of the ramp.
    4. Click Play, and check all of your calculations on the GRAPH tab.

Sliding with Friction

Friction is a general term for forces that oppose motion. Friction is usually caused by the roughness of the surfaces and interactions at the molecular level. The coefficient of friction for a pair of surfaces is a measure of how strong the force of friction between them is. For example, the coefficient of friction between rubber-soled shoes and linoleum is much higher than the coefficient of friction between an ice-skater's blade and the ice.

  1. Click Reset. For Ramp 1, select a Rubber block on a Wood ramp with an Angle of 50°. For Ramp 2, select a Wood block on a Wood ramp, also with an Angle of 50°.
    1. Which block do you think will encounter more friction as it slides?
    2. Which block do you think will slide faster and reach the bottom first?
    3. Click Play to test your predictions. Were you correct?
    4. Select the ENERGY tab. In addition to the previous two bars, there is now a red bar representing the energy lost due to friction. Which block lost more energy to friction?
    5. The energy that was not lost to friction was changed to kinetic energy. Which block had more kinetic energy and was going faster when it reached the bottom of the ramp?
    6. Turn on Show coefficient of friction for both ramps. Which combination of materials had a higher coefficient of friction?
  2. Click Reset. Remove the block from the Ramp 2, and change the Ramp 1 Angle to 30°.
    1. Press Play and describe what happens.
    2. You should have found that the object did not slide at all. The ramp is not steep enough to overcome the frictional force, so no movement occurs. Adjust the Angle until the plane is just barely steep enough for the block to slide down.
    3. What is the greatest angle the ramp can have and still have no movement?
    4. Use a calculator to find the sine, cosine, and tangent of this angle. Which of these three trigonometric value is similar to the coefficient of friction for a Rubber block on a Wood ramp?
    5. Select different materials, and see if the relationship you found persists.
    6. Challenge: Based on what you have seen, describe how you would experimentally determine the coefficient of friction for a combination of materials.