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 27 degrees above the horizontal. The box has a mass of 25.3 kg, and the coefficient of friction between box and floor is 0.268. The acceleration of gravity is 9.8 m/s^2

Find the acceleration of the box.
Answer in units of m/s^2

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 27 degrees above the horizontal. The box has a mass of 25.3 kg, and the coefficient of friction between box and floor is 0.268. The acceleration of gravity is 9.8 m/s^2 Find the acceleration of the box. Answer in units of m/s^2

Explanation / Answer

sum forces in the y

N - m g + F sin theta = 0

N = m g - F sin theta = 25.3*9.81 - 160*sin(27 degrees)= 175.6 N

sum in the x

F cos theta - friction = m a

but friction = u N

160*cos(27 degrees) - 0.268*175.6 = 25.3*a

a= 3.77 m/s^2

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