A delivery company has just unloaded a 500 N crate full of home exercise equipme

Question

A delivery company has just unloaded a 500 N crate full of home exercise equipment in your level driveway. Suppose you try to move the crate by pulling upward on the rope at an angle of 30 above the horizontal. How hard do you have to pull to keep the crate moving with constant velocity? Is this easier or harder than pulling horizontally? For this crate the coefficient of kinetic friction, k , is 0.40.

If the coefficient of static friction s is 0.46, how hard do you have to pull on the crate initially to get it moving if you pull upward on the rope at an angle of 20 above the horizontal

Explanation / Answer

k =0.40
W = 500 N

Friction Force Fs = k * (W - T*sin(30))
If the Crate is moving with constant Velocity, Acceleration = 0

T*cos(30) - Fs = 0
T* cos(30) = Fs
T* cos(30) = k * (W - T*sin(30))
Substituing Values,
T* cos(30) = 0.4 * (500 - T*sin(30))
T = 187.6 N
Force with which needed to pull, T = 187.6 N

It is easier to pull this was than pulling horizontally.

Force needed initially to get it moving ,
F* cos(20) = 0.46 * (500 - F*sin(20))
F = 209.6 N

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