ROLLIN’ ON AN INCLINE Name______________________________

Name______________________________

Name______________________________

A ball is rolled down a hill. Sketch a reasonable graph of the distances the ball is from the top of the hill versus time in seconds.

To see if your sketch is correct, a motion detector unit (CBR) will collect data as a ball is rolled down an incline plane and display a graph.

For this experiment you will need the following equipment:

CBR unit

TI-83 plus (If using a TI-82, download the ranger program from the CBR by pressing the button that shows the type of calculator you are using.)

Ball (Basketball works the best)

Plank

Board protractor

Part I Experiment Setup:

Use the following diagram to simulate a ball rolling down a hill. Measure the angle of inclination using the board protractor. Three people are needed to run the simulation. One person operates the calculator, the other lets go of the ball and the third catches the ball before it hits the CBR.

CBR

Connect the CBR to your calculator. On your calculator, press APPS, CBL/CBR. Press enter when instructed on screen. Choose RANGER, SETUP/SAMPLE. On the following screen, change: REALTIME to “no”, TIME(S) to 5, BEGIN ON to [TRIGGER] and UNITS to FEET. After making these changes move the cursor up to the top right of the screen to START NOW. Collect the data by following the instructions on the screens to follow. When satisfied with the data collections, hit enter and choose PLOT TOOLS, then SELECT DOMAIN. Choose the part of the graph that modeled the situation. Exit program when satisfied with the data collection. The program has transferred the data into L1: time, L2: distance, L3: velocity L4: acceleration.

Part II Analysis of Data

Make a scatter plot of distance vs. time. Make a sketch of the graph and show the window used. Label the axes. Do not connect the dots.

Use the scatter plot to verbally describe how the object fell.

Find a quadratic equation of best fit by using the QuadReg found under the STAT key on your calculator. Use the following commands in order to place the equation into Y1:

Sketch the graph of the quadratic on the graph of the scatter plot.

If the ball has no initial velocity and is not subject to forces such as air resistance, surface friction and moment of inertia, the position x of the ball with respect to the time t can be modeled by the quadratic equation: s(t) = -1/2 g(sin Ө)t² + s₀¸ where s₀ is the initial height of the object, g is the acceleration due to gravity (-32 feet per sec²), and Ө is the angle of the inclined plane. How close did your equation come to this one?