Two blocks on a frictionless surface; find the force

[Peter Halsall]

Homework Statement

Two blocks, A and B , are being pushed on a frictionless surface by a froce of 30 N to the right, .Block A has a mass of 2.0kg, Block B, being pushed by Block A is 4.0kg. Calculate the magnitude of the force that block B exerts on Block A.

Homework Equations

f=ma

The Attempt at a Solution

If The total force pushing the blocks as a system is 30 N, then if you treat the objects as individuals 20 N of the force is provided by Block B and 10 N by Block A. So 20 N is the magnitude of the force that Block B exerts on Block A

 

[BvU]

Is fine, but can you express it more formally in terms of $F = ma$ for the ensemble and for each of the blocks ?

 

[Peter Halsall]

Is fine, but can you express it more formally in terms of $F = ma$ for the ensemble and for each of the blocks ?

I'm sorry, I don't understand what your asking, do you want me to prove it using Newton's 2nd law?

 

[BvU]

Yes. F = ma for the total, a is the same for A and B so with F = ma for B the force needed to accelerate B is the 20 N you found. And from Newton 3 B exerts a reaction force of the same magnitude on A.