Question

1. An Atwood Machine consists of weights attached to the two ends of a pulley. For this machine, the pulley is a thin disk which has a radius of 2m, mass 1 is 8 kg and mass 2 is 5 kg, and both masses start at 5 meters above the ground. When we release the system from rest: How fast will mass 1 be moving right before it hits the ground? b. How fast will mass 2 be moving right at that time? C. What will the angular velocity of the pulley be at that time? d. How many degrees will the pulley turn through this process? a. R g 2

Answer 1

here,

the radius of pulley , r = 2 m

m1 = 8 kg

m2 = 5 kg

s = 5 m

the acceleration of system , a = net force /effective mass

a = ( m1 - m2) * g /(m1 + m2)

a = ( 8 - 5) * 9.81 /(8 + 5) m/s^2

a = 2.26 m/s^2

a)

the speed of first mass , v1 = sqrt(2*a * s)

v1 = sqrt(2 * 2.26 * 5) m/s = 4.76 m/s

b)

the speed of blocks is same

the speed of mass 2 is 4.76 m/s

c)

the angular velocity of the pulley , w = v/r

w = 4.76 /2 rad/s = 2.38 rad/s

d)

the angle covered , theta = s /r

theta = 5 /2 rad = 2.5 rad= 143.3 degree