This is a physics question

Question

A 6.00 kg block rests on a plane with a coefficient of friction of 0.10 and set at a 30-degree angle with respect to the horizontal. It is attached to a rope wrapped around a 4.66 kg drum with a radius of 0.50 m that is free to rotate (without friction)about its axis. Determine the speed of the block at the base of the ramp if it travels 1.5 meters down the incline when released from rest. Use either the principles of rotational dynamics or rotational energy to solve this problem.

Answer 1

Using energy: E_{P, B} - F_fd = E_K,B + E_K,D (potential energy loss of block - frictional work = kinetic energy of the block + rotational kinetic energy of the drum. We are solving for v of the block and the velocity of the rope at the edge of the drum.

m_Bgh - F_fd = (1/2)m_Bv² + (1/2)Iω²

We know that h = dsinθ = d/2, I_D = (1/2)m_Dr² ,(assuming drum is a solid cylinder) ,ω = v/r, and F_f = mgμcosθ

m_Bgd/2 - mgμcos(30) = (1/2)m_Bv² + 1/2((1/2)m_Dr²)(v/r)² (last term is (1/4)m_Dv²)

Now, plug in and solve for v.

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