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(a) The block has a weight of (27.0 kg) g, and the normal force of the surface pushing upward on the block has the same magnitude, so that static friction exerts a maximum force of
µ (27.0 kg) g = 70.0 N
where µ is the coefficient of static friction. Solving for µ gives
µ = (70.0 N) / ((27.0 kg) g) ≈ 0.265
(b) As it's moving, the block still has the same weight and thus feels the same normal force, (27.0 kg) g. In order to move at a constant speed, kinetic friction must exert the same force as the push, so
µ (27.0 kg) g = 64.0 N
where µ is now the coefficient of kinetic friction. Solve for µ :
µ = (64.0 N) / ((27.0 kg) g) ≈ 0.242