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 71.0 N at an angle of 26.0° 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 ty-axis is up along the page.) magnitude direction Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m/s2 ocounterclockwise from the +x-axis (b) The student now starts moving the box up a 10.0° incline, keeping her 71.0 N force directed at 26.0° 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 ty-axis is upwards and perpendicular to the incline.) magnitude direction m/s2 o counterclockwise from the incline

Explanation / Answer

(A) in vertical,

N + T sin26 - m g = 0

N= (24 x 9.8) - (71 sin26)

N = 204 N  

fk = uk N = 0.300 x 204 = 61.22 N  

in horizontal,

(71 cos26) - 61.22 = 24 a

a = 0.108 m/s^2 ....Ans

  
direction = 0 deg  

(B) N - m g cos10 + 71 sin26 = 0

N = 200.5 N  

fk = uk N = 60.15 N  

71 cos26 - 60.15 - (24 x 9.8x sin10) = 24 a

a = - 1.55 m/s^2

Magnitude = 1.55 m/s^2

direction = 180 deg

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