A crate of weight W = 531 lb has been attached to a pickup truck via a rope whos

Question

A crate of weight W = 531 lb has been attached to a pickup truck via a rope whose tensile strength is T max = 341 lb. If the truck and crate start at rest with ? = 34

Before taking any other action, draw a FBD of the crate. There are two possibilities to consider. The first is that the static friction coefficient is so high that the rope breaks before the crate starts moving. This can be examined as a static problem, and the tension in the rope can be written from the equilibrium equations as a function of mus, mg, and theta. Do this and verify that the tension under this limiting case is less than the breaking strength. The premise of the second case is that the rope has survived the transition from stationary to accelerating object and the friction is kinetic. Use the equations of motion to solve for acceleration as a function of g, T, mg, muk and theta and evaluate the result for T = T max.

Explanation / Answer

w = 531 lb = 241 N

m = w/g = 24.6 kg

Tmax = 341 lb = 154.814 N

Fnet = Tmax*cos(34) - (241 - Tmax*sin(34) )*mue_k

Fnet = 91.28 N

m*a = 91.28

a = 91.28/24.6 = 3.71 m/s^2 = 12.17 ft/s^2

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