The device pictured is similar to Atwood\'s machine described in Example 2.2-1:
ID: 1854289 • Letter: T
Question
The device pictured is similar to Atwood's machine described in Example 2.2-1: The masses of the pulleys, friction at the bearings, and extensibility of the cords may be neglected. The masses are released from rest. (a) Show that m3 will remain at rest provided 4/m3 = I/m1 + I/m2 and find the corresponding accelerations of m2 and m1. Ans.: a2 = - a1 = m2 - m1/m2 + m1 g. Show that if = m3 = m1 - m2, m3 will move downward with an acceleration .Show that the angular momentum of the particle in Example 2.2-5 is constant.Explanation / Answer
a)Tension in cord attached to m1 and m2 is T ,than m1g-T=m1a eq (1 T-m2g=m2a eq(2 or eq(1)/m1-eq(2)/m2 than g-(T/m1)=(T/m2)-g eq(3 and if m3 is not moving ;than 2T=m3g T=m3g/2 so g-(T/m1)=(T/m2)-g g-(m3g/2m1)=(m3g/2m2)-g 2/m3=1/(2*m2)+1/(2*m1) 4/m3=1/(m2)+1/(m1) proved eq(1)+eq(2) (m1-m2)g=(m1+m2)a a=(m1-m2)g/(m1+m2) a1=a=-a2=(m1-m2)g/(m1+m2)