Objective: To investigate through mathematics the force(s) acting on an object sliding or rolling down an incline plane.

Background information: A familiar physics formula states that F = ma, where F is force(s) acting on an object, m = mass, and a = acceleration due to gravity. When you have motion on an incline, the force includes the weight (which is a product of mass and gravity) and the angle at which the plane is inclined. Therefore,

In this experiment we will measure the acceleration, a, for different incline angles, .

Materials Needed: 

• 6-foot (or longer) ramp
• Empty coffee can - each group may use a different size can or they may all use the same size - larger cans may provide better data
• Large protractor - gravity protractor, if possible
• CBR
• Graphing Calculator
• Table, chair or stack of books to rest incline plane at different angles

Recommended Group Size: 3

One student to initiate motion, one to operate CBR & calculator & one to record data

Procedure: Part I

1. Set up the CBR on the calculator you will use. Download the correct RANGER version.
   Settings: Realtime=no, Time=3, Display=Dist, Begin on=enter, Smoothing=none, Units=Meters
   
2. Prop the board at different angles on books, a chair, a desk or a table. Use the protractor to measure the angles carefully. Set the CBR at the top of the board. Place the coffee can about a foot away from the CBR. Release the can and let it roll down the incline. DO NOT PUSH IT.
3. Look at the graph on the calculator. Assume that the upward sloped curve on the graph is the right half of a parabola. Choose 2 data points, P1 and P2, (time, distance). Choose the first on the vertex of the parabola, and the other about 1/4 of the way from the top of the incline. See the sample graph below. Record these in the table.

   

4. Repeat steps 2 & 3 for all angle measures 5° to 25° in increments of 5°.
   

   q	Point 1 (t1, d1)	Point 2 (t2, d2)	t = t2 – t1	s = d2 – d1
   5°
   10°
   15°
   20°
   25°

5. Use the values from the above table to fill in the table below. NOTE: Be sure you are in the correct mode! Input sinq values into list 1 in your graphing utility, a values into list 2, and graph a scatter plot of the data using STATPLOT.  Using STAT, CALC, find the regression line for your data and graph it along with your scatter plot.
   

   q	sinq	a
   5°
   10°
   15°
   20°
   25°

6. Predicting what will occur with data points beyond the collected information using the regression line equation is called “linear extrapolation”. Use linear extrapolation to find the expected a value for a q= 90°. Fill in the empty row of the chart with this information.
   • What position would the board be in at this angle?
   • How does this a value related to the acceleration due to gravity = 9.8 m/sec²
   • Is gravity the only force acting on this object?

Procedure: Part II

1. Use the same settings on the CBR as you did in part I for the first two angles. After that you may want to change time from 3 seconds to 2 seconds.
2. Set up the incline and CBR as you did in part I also. This time, place the can upright on the board. Release it, and let it slide down the incline.
3. Look at the graph on the calculator. Assume that the upward sloped curve on the graph is the right half of a parabola. Choose 2 data points, P1 and P2, (time, distance).  Choose the first on the vertex of the parabola, and the other about ¼ of the way from the top of the incline. Record these in the table.
4. Repeat steps 2 & 3 for all angle measures 20° to 45° in increments of 5°.
   
   

   q	Point 1 (t1, d1)	Point 2 (t2, d2)	t = t2 – t1	s = d2 – d1
   20°
   25°
   30°
   35°
   40°
   45°

5. Use the values from the above table to fill in the table below. NOTE: Be sure you are in the correct mode! Input sinq values into list 1 in your graphing utility, a values into list 2, and graph a scatter plot of the data using STATPLOT. Using STAT, CALC, find the regression line for your data and graph it along with your scatter plot.
   
   

   q	sinq	a
   20°
   25°
   30°
   35°
   40°
   45°

6. Use linear extrapolation to find the expected a value for a q = 90°. Fill in the empty row of the chart with this information.