Determine the force P to cause the motion to impend. Take masses of the block A & B as 8 kg & 4 kg respectively and the coefficient of sliding friction as 0.3. The force P and the rope are parallel to the inclined plane. Assume frictionless pulley.[F…

Question

Q.5 (A) Determine the force P to cause the motion to impend. Take masses of the block A & B as 8 kg & 4 kg respectively and the coefficient of sliding friction as 0.3. The force P and the rope are parallel to the inclined plane. Assume frictionless pulley. [Figure: an incline rising to the right at 30° to the horizontal. A frictionless pulley is fixed at the upper end of the incline. Block A (lower on the incline) and block B (higher up) both rest on the incline. A rope from the upper side of A runs up parallel to the incline, over the pulley, and comes back down parallel to the incline to block B. Force P pulls A down the incline, parallel to it.]

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Given: m_A = 8 kg ( W_A = 78.48 N), m_B = 4 kg ( W_B = 39.24 N), μ = 0.3 , θ = 30^° . When P pulls A down the plane, the rope pulls B up the plane. Friction opposes each motion. Block B (impending motion up the plane): N_B = 39.24cos30^° = 33.98 N, F_B = 0.3 × 33.98 = 10.19 N (down the plane) T = W_Bsin30^° + F_B = 19.62 + 10.19 = 29.81 N Block A (impending motion down the plane): N_A = 78.48cos30^° = 67.97 N, F_A = 0.3 × 67.97 = 20.39 N (up the plane) Along the plane: P + W_Asin30^° = T + F_A ⇒ P + 39.24 = 29.81 + 20.39 Answer: P = 10.96 N (down the plane).

Determine the force P to cause the motion to impend. Take masses of the block A & B as 8 kg & 4 kg respectively and the coefficient of sliding friction as 0.3. The force P and the rope are parallel to the inclined plane. Assume frictionless pulley.[F…

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