tension in vertical string below table = T1
m1 a = m1 g - T1
so
T1 = m1 (g-a)
tension in horizontal string above table = T2
m2 a = T2 - m2 g mu
so
T2 = m2 (a + mu g)
then
( T2 - T1 )R = I alpha
but alpha R = a
so
(T2 - T1)R = I a/R
or
T1-T2 = I a /R^2
T1 -m2(a + mu g) = I a /R^2
m1 (g-a) - m2(a + mu g) = I a /R^2
- m1 a -m2 a - Ia/R^2 = -m1 g + mu m2 g
a (m1 + m2 + I/R^2) = g (m1 - mu m2)
a = g (m1 - mu m2) / (m1 + m2 + I/R^2)
A pulley of mass mp , radius R , and moment of inertia about its center of mass Ic , is attached to the edge of a table. An inextensible string of negligible mass is wrapped around the pulley and attached on one end to block 1 that hangs over the edge of the table. The other end of the string is attached to block 2 which slides along a table. The coefficient of sliding friction between the table and the block 2 is μk . Block 1 has mass m1 and block 2 has mass m2 , with m1>μkm2 . At time t=0 , the blocks are released from rest. At time t=t1 , block 1 hits the ground. Let g denote the gravitational acceleration near the surface of the earth.
(a) Find the magnitude of the linear acceleration of the blocks. Express your answer in terms of m1 , m2, Ic, R, μk and g as needed (enter m_1 for m1, m_2 for m2, I_c for Ic, R for R, mu_k for μk and g for g).
(b) How far did the block 1 fall before hitting the ground? Express your answer in terms of m1 , m2, Ic, R, μk, t1 and g as needed (enter m_1 for m1, m_2 for m2, I_c for Ic, R for R, mu_k for μk, t_1 for t1 and g for g).
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