A 2 kg block A is placed on a 5 kg block B. The ground is smooth and coefficient of static friction between A and B is 0.4. A horizontal force F is applied on B. Take g = 10 m/s². The maximum value of F for which there is no slipping is:
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Question

A 2 kg block A is placed on a 5 kg block B. The ground is smooth and coefficient of static friction between A and B is 0.4. A horizontal force F is applied on B. Take g = 10 m/s². The maximum value of F for which there is no slipping is:

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G1 Physics · Accepted Answer

If the blocks move together, a = F/(2+5) = F/7. The only horizontal force on the upper block is friction, so f = 2a. Maximum static friction is fₘₐₓ = μₛmg = 0.4×2×10 = 8 N. Thus 2a ≤ 8 ⇒ a ≤ 4 m/s². Hence Fₘₐₓ = 7×4 = 28 N.