Figure 5.58 shows two masses hanging from a string running over a pulley. Such a

Question

Figure 5.58 shows two masses hanging from a string running over a pulley. Such a device can be used to measure the acceleration of gravity; it is then called Atwood's machine. If the masses are nearly equal, then the acceleration a of the masses will be much smaller than g; that makes it convenient to measure a and then to calculate g by means of Eq. (5.44). Suppose that an experimenter using masses m1 - 400.0 g and m2 - 402.0 g finds that the masses move a distance of 0.50 m in 6.4 s starting from rest. What value of g does this imply? Assume the pulley is massless. FIGURE 5.58 Two masses and a pulley.

Explanation / Answer

The masses have moved .5 m in 6.4 s, so 1/2a(6.4)^2 = .5, and a=1/(6.4)^2 = .0244 m/s/s. Since a is equal to (m1-m2)/(m1+m2), this implies a value of g of .0244*(400+402)/2 = 9.79 m/s.

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