59PredictCalculate Atwoods Machine The two masses m 50 kg a

59.Predict/Calculate Atwood\'s Machine The two masses (m| = 5.0 kg and m2 = 3.0 kg) in the Atwood\'s machine shown in FIGURE 10-33 are released from rest, with m at a height of 0.75 m above the floor. When m, hits the ground its speed is 1.8 m/s. Assuming that the pulley is a uniform disk with a radius of 12 cm, (a) outline a strategy that allows you to find the mass of the pul- ley. (b) Implement the strategy given in part (a) and determine /m 2 the pulley\'s mass. FIGURE 10-33 Problem 59

Solution

Given,

m1 = 5 kg ; m2 = 3 kg ; h = 0.75 m ; v = 1.8 m/s ; R = 12 cm = 0.12 m

a)We can find the mass of the pulley using conservation of energy.

We can calculate the energies of (PE + KE) of the two masses and then deduce for the rotational KE of the pulley and find out the mass.

b)PE1 = 5 x 9.8 x 0.75 = 36.75 J

KE1 = 1/2 m v^2 = 0.5 x 5 x 1.8^2 = 8.1 J

PE2 = m2 g h = 3 x 9.8 x 0.75 = 22.05 J

KE2 = 0.5 x 3 x 1.8^2 = 4.86 J

from conservation of energy

PE1 = KE1 + KE2 + KE2 + KE(pulley)

KE(pulley) = 36.75 - (8.1 + 22.05 + 4.86) = 1.74 J

1/2 I w^2 = 1.74 J

w = v/R = 1.8/0.12 = 15 rad/s

I = 1/2 M R^2 = 0.5 x M 0.12^2 = 0.0072 M

0.5 x 0.0072 M x 15 = 1.74

M = 1.74/0.054 = 32.22 kg

Hence, M = 32.22 kg