Force question: Boxes A and B are in contact...
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# Force question: Boxes A and B are in contact...

[From: ] [author: ] [Date: 12-06-12] [Hit: ]
0 kg. A horizontal force of 100 N is exerted on box A. What is the magnitude of the force that box A exerts on box B?I know the answer is 20 N (back of the book).........
Boxes A and B are in contact on a horizontal, frictionless surface. Box A has mass 20.0 kg and Box B has mass 5.0 kg. A horizontal force of 100 N is exerted on box A. What is the magnitude of the force that box A exerts on box B?

I know the answer is 20 N (back of the book)... I am just trying to understand the process to get there. We literally just learned f=ma and no other complex equations, so I'm quite lost as to how to get 20 N. I would really appreciate it if someone could help me asap!

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Both will accelerate at the same magnitude if they stay in contact. Find the rate at which both boxes will accelerate using F = ma...

a = F/m = (100 N)/(20.0 kg + 5.0 kg) = 4 m/s²

So you know Box B's mass and acceleration, and since the applied force is on A, the only force acting on Box B is the force Box A is exerting on it, so solve for it.

F = ma
F = (5.0 kg)(4 m/s²)
F = 20 N

You could also figure it out through box A. You know it's mass, and you know how much it accelerates. You know a 100 N force is being applied, but another force exists in the opposite direction of the motion: the force box B is exerting onto box A. So...

(100 N - F) = ma
100 N - F = (20.0 kg)(4 m/s²)
100 N - F = 80 N
F = 20 N

By Newton's Third Law, this is also the force A exerts onto B, so 20 N is the answer.

Either way works.
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