One may study Newton’s second law using a device known as Atwood’s machine, shown below. It consists of a pulley and two hanging masses. The difference in weight between the two hanging masses determines the net force acting on the system. This net force accelerates both of the hanging masses; the heavier mass is accelerated downward and the lighter mass is accelerated upward. This system is convenient for studying motion under constant acceleration because we can make the motion much slower, and easier to measure, than if we simply allowed objects to fall freely under the influence of gravity.
atwood machine [pic]
In the discussion which follows m1 is less than m2so that m1 accelerates upward and m2 accelerates downward. According to Newton’s Second Law, the net force on the entire system provides the acceleration for the entire system (m1 and m2 together). The forces acting on the two masses are mainly their weights, m1g and m2g. Both of these forces act downward, but because of the pulley, they act in opposite directions as far as the motion of the masses and the string are concerned. There is also some friction in the pulley, which tends to oppose the motion. So
Fnet= m2g –m1g – F fric(2)
We can measure the frictional force by first making m1 and m2 equal so the apparatus “balances”, then adding just enough mass mf to one side (use the m1side) to overcome the friction. Then F F fric= m gf(3)
Fnet = m2–m1–mfg(5)
The total mass of the system is m1 + m2, so Newton’s Second law predicts theoretically Fneta=Fnet/ M total=(m2-m1-m)g/m1+m2(6)
In this experiment, you will determine the acceleration a experimentally for various combinations of m1 and m2, by measuring the time t requred for m2 to “fall” a distance y, and using the familiar constant-acceleration equation
y=1/2 at^2 (7)
Part 1. Total mass is...