Determining g on an Incline

Introduction

During the early part of the seventeenth century, Galileo experimentally examined the concept of acceleration. One of his goals was to learn more about freely falling objects. Unfortunately, his timing devices were not precise enough to allow him to study free fall directly. Therefore, he decided to limit the acceleration by using fluids, inclined planes, and pendulums. In this lab exercise, you will see how the acceleration of a rolling ball or cart depends on the ramp angle. Then, you will use your data to extrapolate to the acceleration on a vertical “ramp;” that is, the acceleration of a ball in free fall.

If the angle of an incline with the horizontal is small, a cart rolling down the incline moves slowly and can be easily timed. Using time and position data, it is possible to calculate the acceleration of the cart. When the angle of the incline is increased, the acceleration also increases. The acceleration is directly proportional to the sine of the incline angle, (θ). A graph of acceleration versus sin(θ) can be extrapolated to a point where the value of sin(θ) is 1. When sin(θ) is 1, the angle of the incline is 90°. This is equivalent to free fall. The acceleration during free fall can then be determined from the graph.

Objectives

• Use a Motion Detector to measure the speed and acceleration of a cart rolling down an incline.
• Determine the mathematical relationship between the angle of an incline and the acceleration of a cart rolling down the ramp.
• Determine the value of free fall acceleration, g, by extrapolating the acceleration vs. sine of track angle graph.
• Determine if an extrapolation of the acceleration vs. sine of track angle is valid.