Effect on velocity if force stays constant and mass is changed

[bestusername]

(solved) Effect on velocity if force stays constant and mass is changed

Homework Statement

A cannon exerts a constant force on an object. If the mass of the object is doubled, how is the velocity changed

Homework Equations

Fnet = ma; v = v + at

The Attempt at a Solution

i solved for a, so a = Fnet/m
so v = fnet/m * t

so the new velocity is v/2?

but the answer says it is v/square root 2

 

[jgens]

The best way to think of this problem is probably in terms of energy. We know that the work done on the ball in both instances is going to be W = F*s since the force is constant and the length of the cannon does not change. Now, where does this energy go and can you write an equation for it?

Edit: Hootenanny beat me to it.

 

[Hootenanny]

Expanding on jgens' post, whilst the question states that the force exerted on the ball remains constant, it make no mention of the time. Therefore, we cannot assume that it remains constant. This is why your method fails.

 

[bestusername]

ok thanks. I think got it.

Work = change in energy => kinetic energy = 1/2mv^2
v = sq.rt(2w/m)

 

[jgens]

Well, I'm not sure I would do it that way. Since the work done in each instance is the same, you can write your energy equation as follows:

KE₁ = KE₂

Using that equation, solve for your desired velocity.