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Find the angle the force p makes with horizontal such that the block of mass 4 kg has an acceleration of $10 m/sec^2,$ when it is subjected to a force of 35 N.

$μs=0.7,μk=0.6$

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$$m=4 kg,a=1.0 m/s^2,μ_K=0.6$$

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FBD:

$W = 4 x 9.81 = 39.24 N$

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$∑f_x=0⟹ma+μ_K.N-P \cos θ=0 \\ 4×1.0+0.6 N-35×\cos θ=0 ---(1) \\ ∑f_y=0⟹P \sin θ+N-W=0 \\ 35 \sin θ+N-39.24=0 ---(2)$

From (1) and (2)

$4 + 0.6 (39.24 – 35 \sin θ)-35 \cos θ = 0 \\ 4 + 23.544 – 21 \sin θ – 35 \cos θ = 0 \\ 27.544 = 21 \sin θ + 35 \cos θ \\ Θ = 78.52$

Note: In this problem acceleration in given as 10 m/s but to get $10 m/s^2$ acceleration, force given (35 N) is insufficient. So problem can’t solve.

Hence to solve problem, here acceleration is taken as $1 m/s^2$ instead of $10m/s^2.$

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