A 1,140-N crate is being pushed across a level floor at a constant speed by a fo

Question

A 1,140-N crate is being pushed across a level floor at a constant speed by a force F vector of 220 N at an angle of 20.0 degree below the horizontal, as shown in the figure a below. What is the coefficient of kinetic friction between the crate and the floor? (Enter your answer to at least three decimal places.) If the 220-N force is instead pulling the block at an angle of 20.0 degree above the horizontal, as shown in the figure b, what will be the acceleration of the crate? Assume that the coefficient of friction is the same as that found in part (a). Your response differs from the correct answer by more than 10%. Double check your calculations. m/s^2

Explanation / Answer

A. uk = Ff/N

Vertical force balance

Fy = N - W - F*sin 20 = 0

N = 1140 + 220*sin 20 deg = 1215.24 N

Horizontal force balance

Fx = F*cos 20 - Ff = 0

Ff = 220*cos 20 deg = 206.73

uk = 206.73/1215.24 = 0.170

B. In this case

N = W - F*sin 20 = 1140 - 220*sin20 = 1064.75

Ff = uN = 0.17*1064.75 = 181 N

mass = w/g = 1140/9.81 = 116.21 kg

F = m*ax

ax = (F*cos 20 - Ff)/m = (220*cos 20 deg - 181)/116.21

ax = 0.221 m/sec^2

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