A shravani pulls a 5-kg block along a rough horizontal floor with a force, F, wh

Question

A shravani pulls a 5-kg block along a rough horizontal floor with a force, F, which makes an angle, theta = 30 above the horizontal, as shown. The coefficients of static and kinetic friction between the block and the floor are 0.5 and 0.3 respectively. The block is initially at rest.
a) find the maximum force of static friction that must be overcome by the applied force before the block moves (i found it 19.01N)
b) What value of this applied constant force F is required to move the box along the floor at a constant acceleration of 2.0 m/s^2

Please shows the step and explain throughly

Explanation / Answer

b)

fk = k (m g - F sin30)

F cos30 - fk = m a

F cos30 - k (m g - F sin30) = ma

F * 0.8660254 - 0.3*(5*9.8) + 0.3 * 0.5 * F = 5 * 2

F * (0.8660254 + 0.3 * 0.5) = 5 * 2 + 0.3*(5*9.8)

F = 24.3 N

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