Does Momentum Change in Horizontal Direction When Mass is Lowered?

[Nikkolas]

Homework Statement

You are on a cart going at a constant velocity on a frictionless surface. You toss something off the cart in a direction that is perpendicular to your motion, thus lowering the mass of the cart/you system. Does the speed in the horizontal direction change?

Person 1 says: No, because you exerted a force in the perpendicular direction, thus it doesn't affect the car's horizontal motion.

Person 2 says: Yes, because the total momentum of the system is conserved due to the lack of a net external force, thus the horizontal component of momentum is also conserved, thus the change in mass of the cart automatically increases its speed in the horizontal direction.

Who's right?

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Welcome to PF!

Hi Nikkolas! Welcome to PF!

Tell us which you think is right, and why, and we'll comment on it!

 

[Nikkolas]

I think the second person is right. Conservation of momentum is valid just because there is no external net force acting on the entire system. The momentum in both components should be conserved then. This means that the mass thrown off the cart should be compensated with a greater cart velocity in the direction it was traveling in.

But then again, I can't imagine something accelerating in a certain direction (horizontal in this case) unless a component of the net force was exerted on that something in that direction (there is no horizontal force exerted on either object). I'm honestly stumped.

Hi tiny-tim! Thank you for the welcome and thank you for the advice!

 

[tiny-tim]

Person 2 says: … the horizontal component of momentum is also conserved, thus the change in mass of the cart automatically increases its speed in the horizontal direction.

I think the second person is right. Conservation of momentum is valid just because there is no external net force acting on the entire system. The momentum in both components should be conserved then. This means that the mass thrown off the cart should be compensated with a greater cart velocity in the direction it was traveling in.

(i wish you wouldn't keep saying "the horizontal direction" … both directions are horizontal )

Why should the change in mass of the cart cause a change in the speed of the cart?

 

[Nikkolas]

I apologize. I'll stick to x,y,z. lol.

It shouldn't. Net forces cause accelerations, not changes in mass. If the floor is frictionless and a cart is moving at a constant speed, me removing a mass shouldn't make it go faster or slower. This is what I think, but the conservation of momentum keeps on slapping me in the face.

 

[tiny-tim]

Well, momentum is mass times speed, and Person 2 is saying that conservation of momentum means that lower cart mass means higher cart speed … what is wrong with that?

 

[Nikkolas]

I caught mine and #2's error. I mixed my frames of reference, so I didn't take into consideration the component of the projectile's momentum along the direction in which the cart is traveling. Cool. Number 1 wins. Thank you for the hints, tiny-tim.