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Blocks A and B of masses 19 kg and 15 kg, respectively, are connected by a rope that passes over a light frictionless pulley as shown. Horizontal surface is rough. The static and kinetic friction coefficients are 0.40 and 0.20, respectively. External forces P and Q act on block B as shown. In the figure, the force P is equal to 60 N. What is the approximate maximum value of Q force at which the system remains at rest?​

User KiwiKilian
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Final answer:

To find the maximum value of force Q keeping the system at rest, the static friction must be calculated; however, with a force P already at 60 N, it seems there might be an inconsistency as this exceeds the calculated maximum static friction force of 58.8 N. If P was within limits, Q would need to be less than or equal to 58.8 N.

Step-by-step explanation:

Maximum Value of Force Q for Static Equilibrium

To determine the approximate maximum value of force Q at which the system remains at rest, we need to analyze the forces acting on block B and apply the concept of static friction. The static friction force will be the force that keeps block B from moving until it reaches a certain threshold. This threshold is determined by the static friction coefficient (μ_s = 0.40) and the weight of block B (15 kg × 9.8 m/s²).

First, we calculate the maximum static friction force (f_s_max) for block B:

  • f_s_max = μ_s × Normal force on B
  • f_s_max = 0.40 × (15 kg × 9.8 m/s²)
  • f_s_max = 0.40 × 147 N = 58.8 N

Therefore, the maximum force Q before block B moves is the force at which the static friction is at its maximum, which is 58.8 N. Since we already have a force P of 60 N acting on block B horizontally, it exceeds the static friction limit, indicating that the details provided in the question might contain some inconsistencies.

However, if the details were consistent and P did not exceed f_s_max, the force Q would have to be less than or equal to the maximum static friction force so that P + Q ≤ f_s_max for the system to remain at rest.

User PeterKA
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