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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 10m/sec2, when it is subjected to a force of 35 N. μs=0.7, μk=0.6
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First draw the Free Body Diagram (FBD) of the body.

Since, the body is in motion, kinetic friction will be taken into consideration.

SInce, the body is in equilibrium along vertical direction, write equilibrium equation along vertical direction.

$\sum F_y = 0$

$\therefore 35 sin \theta + N = 40$

$\therefore 35 sin \theta = 40 - N$   ...(i)

Also, use Newton's second law along horizontal direction.

$\sum F_x = ma$

$\therefore 35 cos \theta - \mu_kN = 4 \times 10 = 40$

$\therefore 35 cos \theta = 40 + 0.6 \times N$   ...(ii)

Squaring equations (i) and (ii) and then adding, we get,

$35^2 = (40 - N)^2 + (40 + 0.6N)^2$

Solving, we get,

N = 19

Put N = 19 in eqn (1), we get,

$\theta = 37 ^0 $

Hence, the angle is 37 degrees.

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