Two blocks (P and Q) with respectively masses 2 kg and 1.5 kg are joined by a massless thread. These blocks are mounted on a frictionless pulley which is fixed on the edge of a cube (S), as shown in the figure below. Block P is positioned on the top surface which has no friction and block Q is in c…

Question

Two blocks (P and Q) with respectively masses 2 kg and 1.5 kg are joined by a massless thread. These blocks are mounted on a frictionless pulley which is fixed on the edge of a cube (S), as shown in the figure below. Block P is positioned on the top surface which has no friction and block Q is in contact with side-surface, having coefficient friction μ. The cube (S) moves towards the right with acceleration g/2, where g is gravitational acceleration. During this movement the block P and Q remain stationary. The value of μ is . (Take g=10 m/s²).

Accepted Answer

(2) 0.67. Idea: ride with the cube. In its frame each block feels a backward pseudo-force ma, and both blocks are in equilibrium. Here a=g/2=5 m/s². Block P, on the frictionless top. Horizontally it feels the thread's pull T towards the pulley and the pseudo-force backwards: T=m_Pa=2×5=10 N. Block Q, against the vertical side face. The pseudo-force presses it into that face, so it supplies the normal force: N=m_Qa=1.5×5=7.5 N. Q vertically. Its weight is m_Qg=1.5×10=15 N, the thread pulls up with T=10 N, and friction must make up the rest: f=15-10=5 N, upward. At the point of holding, f=μ N: μ=5/(7.5)=2/3≈0.67. Note where the normal force comes from: not from gravity, as on a table, but entirely from the cube's acceleration — stop the cube and Q falls.

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