How Does Projectile Mass Affect Exit Speed in Physics?

[dtl42]

[SOLVED] SAT Subject Test in Physics

Homework Statement

Assume that every projectile fired from a toy cannon experiences force F along the length of the barrel. If a projectile of mass M leaves the barrel with speed, V, at what speed will a projectile of mass 2M leave the barrel with?

Homework Equations

F=ma, a=(Vf-Vo)/t

The Attempt at a Solution

The force F, produces acceleration of V/t for mass m, so the same force should produce F=(2m)(v/t), so the velocity equals v/2?

This is a multiple choice question with choices A) v/2, B)v/sqrt(2), C)v, D)2v, E)4v

The book says the answer is B, but gives no explanation.

 

[Doc Al]

The force F, produces acceleration of V/t for mass m, so the same force should produce F=(2m)(v/t), so the velocity equals v/2?

Careful: The time in the barrel is not the same for the two projectiles.

 

[dtl42]

Oh, that's true, so how can I get around that?

 

[Doc Al]

Oh, that's true, so how can I get around that?

How do the accelerations compare? How does final speed (at the end of the barrel) depend on distance and acceleration?

 

[dtl42]

The final speed is Acceleration/Distance, and we know the distance must be the same for both objects. Can we rearrange the v=a/d and substitute it into F=ma?

 

[dtl42]

Wait, v doesn't equal a/d, I don't know what I'm thinking...

 

[dtl42]

Oh, I found out how to do it, just use v^2=2ad and work it out.

EDIT: Sorry for the obnoxious triple post.