First slide
Friction on horizontal surface
Question

The coefficient of friction between the block and the horizontal surface is μ. The block moves towards right under action of horizontal force -F (figure-a). Sometime later another force P is applied to the block making an angle θ (such that tan θ = μ) with vertical as shown in (figure-b). After application of force P, the acceleration of block shall

 

Moderate
Solution

The free body diagram of block in fig. h is as shown.

 N = mg + P cos θ

and acceleration of block

a = F+P sin θ-μ(mg+ P cos θ)m

a = F+P sin θ-sin θcos θ(mg + P cos θ)m = F-μmgm

Hence P does not change acceleration.

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