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# Forces and Newton's laws of motion (SAT) watch

1. This question is from Barron's:

A 20-newton force is pushing two blocks horizontally along a frictionless floor as shown below:

-----------> | 2kg | 8 kg |
F = 20 N

What is the force that the 8kg mass exerts on the 2kg mass?
The answer given in the book is 16N.

I don't understand this.
Help!
2. Note that the two blocks do not move relative to each other, and so the acceleration of the 8kg block is the same as the acceleration of their common centre of mass, which you can calculate very easily from the given information.
3. Yea, so i get that the acceleration is 2 m/s^2.
And then 8*2 = 16 N
(using this logic, the 2kg block exerts 4N force on the 8kg block)

But I had a conceptual doubt in that newton's third law says that "every force has an equal and opposite reaction" so shouldn't both the blocks exert equal force on each other i.e. 20 N?
Yea, so i get that the acceleration is 2 m/s^2.
And then 8*2 = 16 N
(using this logic, the 2kg block exerts 4N force on the 8kg block)

But I had a conceptual doubt in that newton's third law says that "every force has an equal and opposite reaction" so shouldn't both the blocks exert equal force on each other i.e. 20 N?
Not 20N
The 2kg pushes on the 8kg with a force of 16N. You just calculated that. That force gives the 8kg its acceleration. F=ma 16 = 8 x 2
The 8kg pushes back on the 2kg with the same force of 16N (Newton 3rd)

The resultant force on the 2kg is 20N - 16N = 4N
This 4N gives the 2kg mass its acceleration. 4 = 2 x 2

And of course you can also look at it as the 20N giving the combined mass of 10kg an acceleration of 2m/s/s
5. Oh yes, I get it...
Thanks!

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