I only need e and f answered please!! 4) (12 pts.) Two blocks having masses m1 a

Question

I only need e and f answered please!!

4) (12 pts.) Two blocks having masses m1 and m2 are connected to each other by a light cord that passes over two identical frictionless pulleys, each having a moment of inertia I and radius R, as shown in the figure. The arrows show the direction of motion for each block after the system is released from rest. (a) Draw a free body diagram for the system and clearly label your coordinate choices and unit vector directions. (b) Draw a torque diagram for the pulley. Make sure to clearly label what forces are acting on the pulley, where they are acting on the pulley and the direction of the torque that is generated (c Formulate the 2nd Newton's laws for both objects and the dynamical equation for the rotation of the pulley. (d) Find the linear acceleration of the system. Express your answer in terms of known quantities. e Find expressions for the tensions Ti, T2, and T3. Express your answer in terms of known quantities. (f) Show that when the pulleys become massless the acceleration and tensions reduce to those found in the Atwood machine: 2m1m2

Explanation / Answer

for mass 1

m1g - T1 = m1*a

for mass 2

T3 - m2g = m2a

for pulley 1

torque = t = R(T1-T2) = I*apha

for pulley 2

t = R(T2 - T3) = I*alpha

and R*alpha = a

a = (m1-m2)*g/[m1+m2+2I/R^2]

part b )

now pulleys are massless

m1g-T = m1*a

T - m2g = m2*a

by solving this

m1g-m2g = (m1+m2)*a

a = (m1g-m2g)/(m1+m2)

now put the value of a in eq

T = 2m1m2*g/(m1+m2)

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