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To measure the acceleration due to gravity on a distant planet, an astronaut hangs a 0.085-kg ball from the end of a wire. The wire has a length of 1.5 m and a linear density of 3.1 ´ 10-4 kg/m. Us-ing electronic equipment, the astronaut measures the time for a transverse pulse to travel the length of the wire and obtains a value of 0.083 s. The mass of the wire is negligible compared to the mass of the ball. Recalling that the speed, v, of a small-amplitude wave on a string is given by

v=squareroot(F/(m/L))

mball= .085 kg

L= 1.5 m

m/L = 3.1 * 10^-4 kg/m (linear density)

t= 0.083 s

F=Tension=mg= (.085 kg)(9.8 m/s^2) F=.833 N

v=squareroot(.833(3.1*10-4) = 51.8 m/s

v= initial velocity + at

initial velocity=0

51.8 = 0 + a(.083)

51.8/.083 = a

acceleration= 624 m/s^2

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