A student decides to move a box of books into her dormitory room by pulling on a

Question

A student decides to move a box of books into her dormitory room by pulling on a rope attached to the box. She pulls with a force of 160 N at an angle of 32? above the horizontal. The box has a mass of 25.2 kg, and the coefficient of friction between box and floor is 0.275. The acceleration of gravity is 9.8 m/s2 .

a) Find the acceleration of the box. Answer in units of m/s2

b) The student now starts moving the box up a 10.8? incline, keeping her 160 N force directed at 32? above the line of the incline. If the coefficient of friction is unchanged, what is the new acceleration of the box? Answer in units of m/s2

Explanation / Answer

a)N=mg-FSin(theta)=25.2*9.81-160Sin32=162.43N

a=(FCos(theta)-uN)/m=(160Cos(32)-0.275*162.43)/25.2=3.61m/s^2

b)N=25.2*9.81*Cos10.8-160Sin(42.8)=100.04N

a=(160Cos42.8-25,2*9.81Sin10.8-0.275*100.04)/25.2=1.729m/s^2

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