The systems shown below are in equilibrium (with m = 4.80 kg and = 32.0°). If th

Question

The systems shown below are in equilibrium (with m = 4.80 kg and = 32.0°). If the spring scales are calibrated in newtons, what do they read? Ignore the masses of the pulleys and strings and assume the pulleys and the incline are frictionless.

A crate of mass m = 31 kg rides on the bed of a truck attached by a cord to the back of the cab as in the figure. The cord can withstand a maximum tension of 76 N before breaking. Neglecting friction between the crate and truck bed, find the maximum acceleration the truck can have before the cord breaks.
m/s2

Explanation / Answer

a)

reading of spring scale = mg + mg = 2*mg = 2*4.8*9.8 = 94.08 N

b)

reading of spring scale = mg = 4.8*9.8 = 47.04 N

c)

reading of spring scale = mg + mg = 2*mg = 2*4.8*9.8 = 94.08 N

d)

reading of spring scale = mgsin(theta) = 4.8*9.8*sin32 = 24.93 N

2)

The cord can withstand a maximum tension = 76 N

the maximum acceleration the truck can have before the cord breaks = T/m = 76/31 = 2.45 m/s^2

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