APPARATUS
THEORY
Atwood’s Machine
Goals: Observe the relation between force, mass and acceleration. Calculate the acceleration due to gravity. Use a graph to correct data to account for friction.
The Atwood machine is a simple device consisting of two unequal masses that are con- nected by a cord run over a pulley. The larger mass (m2) is suspended above the smaller mass (m1), and sits upon a platform that is equipped with a mechanical trip release. Upon release, the heavier mass accelerates down to a platform a measured distance (h) below. Each group will measure the time (t) required for m2 to move from the upper to the lower platform.
The masses in the Atwood machine are subject to a number of forces, all of which are constant. The net constant force will produce a constant acceleration. We know that a
constant acceleration (a) will cause an object to move a distance equal to (1/2) a t2. If we measure the distance and time we can solve for the acceleration.
2h a = ---- (EQ 1)
t2
A perfect Atwood machine would have a massless and frictionless pulley. In that simpli- fied case the force acting to pull down the heavy mass is F2 = m2g, and the force pulling up due to the lighter mass being pulled down is F1 = m1g. The net force pulling down on the heavy mass would be F = F2 - F1 = (m2 - m1)g. Both masses are accelerated together so Newton’s second law is F = (m2 + m1)a. Combining these two equal expressions for force allows us to solve for the ideal acceleration a = (m2 - m1) g / (m2 + m1).
Our real Atwood machine has a pulley with some mass that resists acceleration and some kinetic friction on the axle of the pulley that reduces the net force pulling down the heavy mass. The mass of the pulley mp is being accelerated by the pull of the string at its rim. We will learn later in the course that a rotating disk provides an equivalent
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DATA COLLECTION
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Atwood’s Machine
additional inertia at its rim equal to half of its mass: mp / 2. For this...