Question

Suppose you are a space traveler, and you land on the surface of a strange new planet. As stated in your Starfleet Manual, your first job is to measure the acceleration due to gravity, g, on this planet. You construct an "Atwood machine", which consists of two masses connected to a pulley by a string of negligible mass, as shown in the figure. One of the masses is m₁ = 50.0 kg and the other is m₂ = 39.0 kg. The pulley is a uniform disk of mass M = 95.0 kg and radius r = 78.0 cm which is mounted on frictionless bearings. When released from rest, the heavier mass moves down 146.6cm in 1.37 s, and there is no slippage of the string on the pulley.

(a)What is the magnitude of the acceleration of the blocks?

(b)What is the value of the acceleration due to gravity (g) on this planet?

(c)What is the weight of m₁ on this planet?

Answer 1

the magnitude of the acceleration of the blocks = a
d = at^2/2, so a = 2d/t^2


To find the value of the acceleration due to gravity (g) on this planet:
for m1: m1*g - T1 = m1*a
for m2: T2 - m2*g = m2*a
for M: (T1 - T2)*r = I*a = (Mr2/2)*(a/r), so T1 - T2 = Ma/2
so m1*g - m2*g = (m1 + m2 + M/2)a
g = (m1 + m2 + M/2)a/(m1 - m2)

the weight of m1 on this planet = m1*g