A 1,400-N crate is being pushed across a level floor at a constant speed by a fo

Question

A 1,400-N crate is being pushed across a level floor at a constant speed by a force

of 250 N at an angle of 20.0° below the horizontal, as shown in the figure a below.

(a) What is the coefficient of kinetic friction between the crate and the floor? (Enter your answer to at least three decimal places.)


(b) If the 250-N force is instead pulling the block at an angle of 20.0° 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).
m/s2

Explanation / Answer

part a )

force in y direction

N - W - Fsin20 = 0

n = 1400 + 250 sin20

n = 1485.51 N

forces in x direction

Fcos20 - f = 0

f = 250 cos20 = 234.92 N

the coefficient of kinetic friction between the crate and floor is

mu = f/n = 234.92/1485.51

mu = 0.158

part b)

here vertical acceleration is zero

forces in y direction = may = 0

Fsin20 + n - W = 0

n = 1400 - 250sin20 = 1314.5 N

friction force = mu*n = 207.7 N

mass of crate = m = 1400/9.8 = 142.86 kg

forces in x direction

a = Fcos20 - f / m = [250cos20 - 207.7]/142.86

a = 0.191 m/s^2

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