Need help Basic Physics question from a competitive test.

[johsun123]

Homework Statement

Two bodies of masses M1& M2 resting on frictionless surface. Bodies touch each other without any friction.
What will be the force between the bodies, If they are pushed from one end with force F and both are accelerating towards other end?
Answer given is (M2 x F)/(M1+M2).
How is it arrived at?

Homework Equations

F= G M1XM2/ distance squared

The Attempt at a Solution

I am stumped. I cannot arrive at this with above equation.

 

[Basic_Physics]

You really need to draw a diagram with the forces and accelerations to solve this one - a free-body diagram.

 

[Bill Nye Tho]

You shouldn't be using Newton's Law of Universal Gravitation here.

When you draw a free body diagram of M1, you'll recognize that there is a resisting force (f) on it from the other mass.

1)

ƩF_x = M₁a

F - f = M₁a


Then draw a free body diagram of M2, which has no resisting force.

2)

ƩF_x = M₂a

F = M₂a




You should understand the fact that both masses will have the same acceleration.

Knowing that detail, you can manipulate your equations in order to solve for the missing force "f."

Start by solving the 2nd equation for acceleration:

a = F/M₂

Plug that back into the 1st equation and you should have:

f = FM₂/(M₁+M₂)

 

[johsun123]

Thank you. It was bugging me.

It looks like a grade 11 question to me.