A worker drags a crate across a factory floor by pulling on a rope tied to the c

Question

A worker drags a crate across a factory floor by pulling on a rope tied to the crate. The worker exerts a force of 415 N on the rope, which is inclined at 29.0 to the horizontal. The floor exerts a horizontal resistive force of 117 N.

a) If the mass of the crate is 87.0 kg calculate the acceleration of the crate in the horizontal direction.

b) If the weight of the crate is 87.0 N calculate the acceleration of the crate in the horizontal direction.

c) If the mass of the crate is 87.0 kg calculate the acceleration of the crate in the vertical direction (if any).

d) If the weight of the crate is 87.0 N calculate the acceleration of the crate in the vertical direction.

Use g = 9.81 m/s2.

show the steps briefly please

Explanation / Answer

Apply Newtons second law to the crate

T cos theta-f = ma

a= T cos theta - f/m = 415 cos29-117/87 = 2.82 m/s^2

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multiply numerator and denominator by g

a= T cos theta - f/mg)* g = 415 cos29-117/87 N) 9.8 = 27.7 m/s^2

(c)

ay = 0

(d)

ay = 0

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