# Explosive motion of two carts away from one another, driven by plunger in one of them

1. Feb 10, 2009

### lolohhi

1. The problem statement, all variables and given/known data
I feel silly posting such a simple problem, but a substantial amount of thinking, Googling, and scouring these forums has not yielded an answer.

2. Relevant equations
Newton's Second Law: F*_net = ma* (where the asterisk denotes a vector quantity)
Newton's Third Law: F*_(A on B) = F*_(B on A)

3. The attempt at a solution
I reasoned that the acceleration of the blue cart remains constant regardless of the mass of the red cart. Given the statement that the red car's acceleration is reduced by a factor of five when its mass is increased by a factor of five (from 250 g to 1.25 kg), according to (F*_net = ma*), I would expect that F*_net on the red cart remains constant. Since the magnitudes of F*_net_red and F*_net_blue must be equal by Newton's Third Law, I reasoned that the force exerted on the blue cart must be the same regardless of the mass of the red cart, given that the net force exerted on the red cart seems to remain constant regardless of its mass. As the mass of the blue cart remains constant, if the net force exerted on it remains so as well, then its acceleration must remain constant, too. To explain the correct answer in which the blue cart moves with greater acceleration when the mass of the red cart is increased, one must assume that the red cart exerts a greater force on the blue cart when the mass of the red cart is increased, which makes no sense to me whatsoever.

Thinking in less abstract and more intuitive terms, I'm still confounded. On the one hand, increasing the mass of the red cart should not increase the force with which its plunger extends, and thus the blue cart should have the same force exerted on it regardless of the mass of the red cart. On the other hand, if I imagine increasing the mass of the red cart to several thousand times its current value, it seems the reaction force of the blue cart pushing against the red cart would not move the red cart at all; if the red cart didn't move, less motion would be "wasted" moving the red cart (if that makes any sense at all) and the blue cart would move away faster than it did when the red cart had a lesser mass.

The correct answer is that the blue cart's acceleration increased by a factor of five when the mass of the red cart was increased by a factor of five. I still don't understand why the blue cart wouldn't move away at the same acceleration regardless of the mass of the red cart. Any assistance you provide will be much appreciated.​

2. Feb 10, 2009

### LowlyPion

Re: Explosive motion of two carts away from one another, driven by plunger in one of

Welcome to PF.

I think you want to think about the Conservation of Momentum.

Before the plunger V = 0 for both.

That means that the momentum of 1 is the opposite of the other after release.

Momentum is M*V so that

M1V1 = M2V2

Masses the same ... Velocities the same.

What happens then when M1 = 5*M2? What must V2 be relative to V1?

5*M2*V1 = M2*V2