Eric Murray, Spring 2006
The magnitude of an object's acceleration down an inclined plane is
a = g sin θ
If the object travels a distance s while descending a distance h, then sin θ = h/s, and
a = g h/s ⇒ g = a s/h
By making multiple measurements of a, you will be able to find a ± Δa, and then calculate g ± Δg. Note that a = g sin θ is only expected when the acceleration of the object is entirely due to gravity. If you find an acceleration of gravity that does not agree with the typical value of 9.8 m/s2 within your measure of experimental error, then you will have to consider systematic errors. You have not studied forces, yet, but two likely systematic errors are acceleration due to a friction force and acceleration due a drag (air resistance) force. The frictional force decreases as the angle θ increases, while the drag force increases with increasing cart speed. If you find that there is systematic error, you should be able to compare your values of g measured at two different angles to decide whether friction or drag is a more reasonable explanation.