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 72.8 N at an angle of 30.0° above the horizontal. The box has a mass of 20.0 kg, and the coefficient of kinetic friction between box and floor is 0.300. (Indicate the direction with the sign of your answer.)

(a) Find the acceleration of the box. (Assume that the +x-axis is to the right and the +y-axis is up along the page.)

(b) The student now starts moving the box up a 10.0° incline, keeping her 72.8 N force directed at 30.0° above the line of the incline. If the coefficient of friction is unchanged, what is the new acceleration of the box? (Assume that the +x-axis is along the incline and the +y-axis is upwards and perpendicular to the incline.)

Explanation / Answer

Fcos(30) - (u(mg-Fsin(30))) = ma ( u =.30, N = mg-Fsin(30) )

72.8*0.865 - (.3*(20*9.8-72.8*1/2)) = 20a

=> a = 0.75 m/s^2

direction is along positive x = 0 degree from the x axis

b)

Fcos(30) - u(mgcos(10)-Fsin(30) ) - mgsin(10) = ma

72.8*0.865 - (.3*(20*9.8*0.98 -72.8*1/2) - 20*9.8*.17 = 20a

a is negative which mean net force is not capable of carring the load hence a = 0 Or box won't move

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