Alex is asked to move two boxes of books in contact with each other and resting

Question

Alex is asked to move two boxes of books in contact with each other and resting on a rough floor. He decides to move them at the same time by pushing on box A with a horizontal pushing force -9.1 N. Here, A has a mass mA = 10.6 kg and B has a mass m 7.0 kg. The contact force between the two boxes is FC The coefficient of kinetic friction between the boxes and the floor is 0.04. Assume FP acts in the +x direction. MA 0in (a) What is the magnitude of the acceleration of the two boxes? m/s2 (b) What is the force exerted on me by mA? In other words, what is the magnitude of the contact force Fc? (c) If Alex were to push from the other side on the 7.0-kg box, what would the new magnitude of Fc be?

Explanation / Answer

Given,

Fp = 9.1 N ; mA = 10.5 kg ; mB = 7 kg ; uk = 0.04

a)Let a be teh acceleration,

The net force acting on the boxes is:

Fnet = Fp - Ff

where Ff is the frictional force

Ff = uk (mA + mB)g = 0.04 x (10.6 + 7) x 9.81 = 6.91 N

Fnet = 9.1 - 6.91 = 2.19 N

Fnet = (mA + mB) a = 2.19

a = 2.19/17.6 = 0.124 m/s^2

Hence, a = 0.124 m/s^2

b)force will be:

FC = uk mB g + mB a

FC = mB (uk g + a) = 7 ( 0.04 x 9.81 + 0.124) = 3.615 N

Hence, Fba = 3.615 N

c)In this case,

FC = uk mA g + mA a = mA (uk g + a)

FC = 10.6 (0.04 x 9.81 + 0.124) = 5.474 N

Hence, FC = 5.474 N

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