002 (part 1 of 2) 10.0 points A student decides to move a box of books into her

Question

002 (part 1 of 2) 10.0 points A student decides to move a box of books into her dormitory room by pulling on a rope at- tached to the box. She pulls with a force of 170 N at an angle of 33 above the horizon- tal. The box has a mass of 26.7 kg, and the coefficient of friction between box and floor is 0.275 The acceleration of gravity is 9.8 m 33 26.7 kg 0.275 Find the acceleration of the box. Answer in units of m/s 003 (part 2 of 2) 10.0 points The student now starts moving the box up a 12.40 incline, keeping her 170 N force directed at 33 above the line of the incline. 33 26.7 kg 12.4 If the coefficient of friction is unchanged,

Explanation / Answer

a)

F*cos(33) - u*N = ma

N = mg - F*sin(33)

So, F*cos(33) - u*(mg - F*sin(33)) =ma

So, a = ( F*cos(33 deg) - u*mg + u*F*sin(33 deg) )/m

So, a = ( 170*cos(33 deg) - 0.275*26.7*9.8 + 0.275*26.7*sin(33 deg)) / 26.7

So, a = 2.79 m/s2 <------answer

b)

Now,

F*cos(33 deg) - u*N - mg*sin(12.4 deg)= ma ------- (1)

N = mg*cos(12.4 deg) - F*sin(33 deg) ------- (2)

So, F*cos(33 deg) - u*(mg*cos(12.4 deg) - F*sin(33 deg)) - mg*sin(12.4 deg) = ma

So, 170*cos(33 deg) - 0.275*(26.7*9.8*cod(12.4 deg) - 170*sin(33 deg)) - 26.7*9.8*sin(12.4 deg) = 26.7*a

So, a = 1.56 m/s2 <-----answer

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