Part I: Incline acceleration
Motion down an incline is a famous experiment that goes back to Galileo. He was one of the first to understand motion with constant acceleration. For instance, he knew that if the object started from rest then its displacement varied like time squared. Later Newton would relate the accelaration of an object to the net force acting on that object. In the absence of friction and air resistance, theory says that the acceleration down an incline is given by
where q is the angle relative to the horizontal and g is 9.8 m/s 2 , the acceleration due to gravity. We will attempt to verify this result by the following experiment.
The flat region indicates the time before the cart is released, the upward sloping region corresponds to the cart accelerating down the track, and the abrupt downward sloping region is where the cart was stopped (before clicking STOP). The pale yellow rectangle was obtained by holding the mouse over a point in Excel.
| Incline data | ||||||||
| Length of track ( ) | ||||||||
| Height ( ) | Angle (degrees) | Theoretical Acceleration ( ) | Experimental Acceleration Trial 1( ) | Experimental Acceleration Trial 2( ) | Experimental Acceleration Trial 3( ) | Average Acceleration ( ) | Standard Deviation ( ) | Percent difference |
| Incline data: Mass variation | |||
| Cart Mass (kg) (inc. block) | Experimental Acceleration (m/s 2 ) (from graph) | Theoretical Acceleration (m/s 2 ) (from eq.) | Percent error |
Part II: The pulley
In the case of the cart on the incline, the cart (in particular its mass) plays a dual role. It is the thing being accelerated, and it is the cause of the acceleration (the gravitational attraction between the mass and that of the earth). Now we will consider a situation in which the cause of the object's acceleration is not its weight.
Cart
Mass (kg)
(inc. block)
Experimental
Acceleration (m/s 2 )
(from graph)
Theoretical
Acceleration (m/s 2 )
(from eq.)