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 78.4 N at an angle of 28.0°above the horizontal. The box has a mass of 24.0 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 78.4 N force directed at 28.0° 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

(A) in vertical,

N + 78.4sin28 = (24 x 9.8)

N = 198.4 N

f = uk N = 59.5 N

in horizontal,

fnet = 78.4 cos28 - 59.5 = 24a

a = 0.405 m/s^2 ......Ans

direction = 0 deg

(b)

N + 78.4 sin28 - (24 x 9.8 x cos10) = 0

N = 194.8 N

f = uk N = 58.45 N

along the incline,

78.4 cos28 - 58.45 - (24 x 9.8 x sin10) = 24 a

a = - 1.25 m/s^2

magnitude = 1.25 m/s^2

direction = 180 deg

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