Question

Find the least horizontal force \( P \) to start motion of any part of the system of three blocks resting upon one another as shown in the figure. The weights of blocks are \( A = 300 \, {N}, B = 100 \, {N}, C = 200 \, {N} \). The coefficient of friction between \( A \) and \( C \) is 0.3, between \( B \) and \( C \) is 0.2 and between \( C \) and the ground is 0.1.

 

• A. 60 N
• B. 90 N
• C. 80 N
• D. 70 N

Hint:

Calculating static friction at each interface is crucial in problems involving stacked objects to understand how much force is needed to cause motion.

Answer 1

The Correct Option is A

Step 1: Calculate the total friction force required to overcome.

Normal force on C = 600 N (sum of all weights)

Friction force on C = 0.1 × 600 N = 60 N

Friction force between B and C = 0.2 × 100 N = 20 N

Friction force between A and C = 0.3 × 200 N = 60 N

Total friction force to overcome = 60 N + 20 N + 60 N = 140 N

Step 2: Assess the minimum force required.

To initiate motion, the applied force P must overcome the total friction force of 140 N. Thus, P must be at least 140 N.