Motion on an Inclined Plane

Purpose: To find the mathematical model for displacement (Dx), velocity (v) and acceleration (a) vs. time for an object on a (fairly) frictionless inclined plane or ramp.

You will either be using a cart and an inclined air track or a ball and a ramp with one photogate at the start and one at the finish. As the cart/ball passes through the first photogate it starts the time and as it passes through the second photogate it stops the time. Find this time for at least 6 different displacements, 3 trials each (displacement is the distance between the photogates). Make sure you always start the cart/ball from rest!!!! Also a small incline makes for larger times and greater accuracy.

Do your hypotheses for each of the mathematical models before you begin the experiment!!!

Data Analysis:

1. Use “Graphical Analysis” to graph “Dx vs t”. Even though Dx is your independent variable, graph it on the y-axis. Find the mathematical model.

2. Instantaneous velocity is given by the slope of the tangent to the “Dx vs t” curve at any particular time. You will be putting your equation or mathematical model for “Dx vs t” into a TI-83 calculator. Follow the instructions here:

http://modeling.asu.edu/Modeling-pub/Mechanics_curriculum/3-Uniform%20a/03_slope-TI.pdf

for finding the slope of the tangent at 6 different times. (time is the x-value on the calculator, velocity is the slope of the tangent.) Make a table of these values. Use “Graphical Analysis” to graph “v vs t”. Find the mathematical model.

3. Acceleration is a=Dv/Dt which is the slope of your “v vs t” graph. Draw an “a vs t” graph and find the mathematical model.

4. Compare the acceleration to the value of the slope in your “Dx vs t” graph. How do these two numbers compare? Write a general equation for Dx in terms of a and t.