Comparing Momentum of Two Carts with Different Masses

[einsteinette]

Hello there, I am having difficulty with this question:

A 0.2 kg plastic cart (Cart a) and a 20 kg (Cart b) lead cart can both roll without friction on a horizontal surface. Equal forces are used to push the two carts forward for a distance of 1 m, starting from rest. Which cart has the greater momentum, after the full 1m?

So I was thinking that since you apply equal forces to push the two carts, Cart A would have a higher velocity. But when you do the momentum of the two carts together, the larger mass of cart B would make up for the difference of velocity. If I'm right about the velocity thing that is.

mava = 0.2Va(>vb)
mbvb = 20Vb(<va)

So the momentum would be somewhat equal?

 

[Doc Al]

So I was thinking that since you apply equal forces to push the two carts, Cart A would have a higher velocity.

That's true, but you need to figure out how much higher is the velocity of Cart A. Hint: Since equal force is exerted for equal distance, what can you say is the same for the two carts after the push?

 

[einsteinette]

The force applied and the rate of deceleration?

 

[Doc Al]

The force applied and the rate of deceleration?

The force is the same but the accelerations are not. But you can use Newton's 2nd law and some kinematics to figure out the velocity of each cart after it is pushed. Then you can compare momentum.

But another way is to recognize what force*distance gives you, and use that to figure out the velocity and momentum.

 

[einsteinette]

Ahh so you mean work done is the same. I think I get it now. Thanks!