### Exploring RampsDr. David R. Burgess

Using the ramp above, collect data and graph the speed at the bottom of the ramp (Final Speed) along the y-axis as each of the following changes are made for a solid ball rolling down a ramp without friction. Find at least five points for each graph. Assume the numbers are exact (don't worry about the ±).

1. Change the length of the ramp without changing the angle.
2. Change the length of the ramp without changing the height at the top of the ramp.
3. Change the angle without changing the length of ramp.
4. Change the angle without changing the height at the top of the ramp.
5. Change the height at the top of the ramp without changing the angle.
6. Change the height at the top of the ramp without changing the length of the ramp.
7. Change the mass without changing the length, angle, or the height of the ramp.

For each graph do the following:

1. Correctly label both axes.
2. State the effect of the variable along the x-axis on the speed at the bottom of the ramp according to the graph.
3. State the variable that is being held constant.
4. Identify all of the variables that change when the x-axis variable is changed. You will need to record all of the variables for each run: height, length, mass, and angle as well as the final speed for each data point.

After looking at all of the information that has been collected, identify the one variable that changes the speed at the bottom of the ramp and explain how you came to that conclusion using this data. This will be the overall conclusion.

Homework Assignment: Hand in the data tables, corresponding graphs (with the accompanying information) and the overall conclusion (with the explanation) at the next class meeting.

To manipulate the ramp place the cursor at the very top corner of the ramp. When you see the hand, hold down the left mouse button and drag the ramp to whatever height, length, or angle that you desire. Sometimes the ramp will "stick" to the arrow cursor and not let go. Move the arrow cursor out of the white box and reload the page. If it is stuck to a hand cursor, stop moving the curser and left click to let go. The initial numbers do not correspond to the pictured ramp! Initially the ramp is really at a height of 3.02 m, a length of 10.45 m, a horizontal distiance of 10 m, and an angle of 16.8 degrees.

Thinking Questions:

1. What is the minimum number of experiments you could do and still come to the same conclusion?
2. Is it possible to keep both the height and the length constant when changing the angle?
3. Is it possible to keep both the angle and the length constant when changing the height?
4. Is it possible to keep both the height and the angle constant when changing the length?
5. What would happen if there was friction?
6. How could this be related to the conservation of energy?