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 FP = 8.5 N. Here A has a mass mA = 10.2 kg and B has a mass mB = 7.0 kg. The contact force between the two boxes is

The coefficient of kinetic friction between the boxes and the floor is 0.02. (Assume

acts in the +x direction.)

(a) What is the magnitude of the acceleration of the two boxes?
1 m/s2

(b) What is the force exerted on mB by mA? In other words what is the magnitude of the contact force

2 N

(c) If Alex were to push from the other side on the 7.0-kg box, what would the new magnitude of

be?
3 N

Tutorial

Supporting Materials

Explanation / Answer

a)

F = ma
as you know.

the friction force pushing back is Ff = uFn
basically the friction coefficient multiplied by the normal force.

So the net force is the force being pushed - Ff

normal force is Fn = mg

so the equation of horizontal net force will be: F = 8.5 - (0.02*9.81*(10.2+7))

F =5.12 N

Now just use F = ma and we get

a = 5.12/(10.2+7) = 0.298 m/s^2

b) the lead box, B, has FC pushing it in the positive direction and kinetic friction acting on it in the negative direction. The acceleration of the box is the common acceleration we just found. So we have

FC ? 0.02?mB?g = mB?0.298

? FC ? 3.4594 N .

c)

If Alex were to push from box B side then

FC ? 0.02?mA?g = mA?0.298

or FC = 5.04 N

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