Two boxes sit side-by-side on a smooth horizontal surface. The lighter box has a

Question

Two boxes sit side-by-side on a smooth horizontal surface. The lighter box has a mass of 5.13 kg, the heavier box has a mass of 7.46 kg.

(a) Find the contact force between these boxes when a horizontal force of 5.2 N is applied to the light box. (in Newtons)

(b) If the 5.2 N force is applied to the heavy box instead, is the contact force between the boxes the same as, greater than, or less than the contact force in part (a)? (greater than, less than, or equal to?)

(c) Verify your answer to part (b) by calculating the contact force in this case. (in Newtons)

Explanation / Answer

By a smooth horizontal surface I assume it is considered frictionless. The 4.94N force will make the combination of two boxes accelerate with an acceleration given by:

a = F / (m1 + m2) = 5.2 / (5.13 + 7.46) = .413 m/s

For part a) look at the forces on the large box. The only force is the force of contact (ie, the force that the small box exerts on the large one). Let's call this force Fc. Newton's 2nd law tells us that

Fc = M_large x a = 7.46 * .413 = 3.081 N.

For part b) look at the forces on the small box. The only force is the contact force Fc. Newt's 2nd tells us that in this case

Fc = M_small x a = 5.13 * .413 = 2.12 N

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