*The acceleration can be calculated using netF = ma or by v = v_o + at.

Using the net F equation gives a = g[sin(θ) - μscos(θ)]. Where a is acceleration, g is the acceleration due to gravity (9.8 m/sec²), θ is the angle of the ramp, μ is the coefficient of friction and s is the distance traveled along the ramp.

Using the kinematics equation gives a = v_f/t. Where a is acceleration, v_f is the final velocity and t is the total time.

Both of them give exactly the same acceleration!

What You Will Do

Using the ramp above monitor the final speed (y-axis) as you change the length, height, angle, friction and mass along the x-axis as indicated below. Find at least five points for each of the graphs. Don't worry about calcualting uncertainty or getting the ±. Also, the numbers don't have to exact each time, just get them as close as you can without spending a lot of time worrying about the last decimal place.

More Details

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.

Thinking Questions (not to be handed in):

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?