Finding the mean net force during a collision

[youmei0426]

Homework Statement

Homework Equations

F=ma=mv/t[/B]

The Attempt at a Solution

I used the equation F=mv/t, in which I find the change in velocity and change in time before and after the collision. The change in time is t2-t1, but the problem comes when I am calculating the change in velocity. Shouldn't the change be (v-u)? The answer is D, in which the velocity becomes the sum of u and v, and I don't understand why. Thanks in advance!

 

[PhanthomJay]

velocity is a vector, and as such , it has both magnitude and direction.

 

[ZapperZ]

This is what it looks like visually:

As PhantomJay has stated, you need to actually understand what the equation you are using really means and what each of the variables are. The FULL equation here is:

$$\vec{F} = m \frac{\Delta \vec{v}}{\Delta t}$$

Since velocity is a vector, the CHANGE in velocity will require that you know the directions of the initial and final velocity. If we designate +x direction as the same direction as "u" (as in the fig), then the final velocity is "-v".

This, Δv = -vi - ui = - (v+u)i;

and
Δt = t₂ - t₁

This means that the force exerted by the wall is

$$\vec{F} = -m \frac{v+u}{t_2 - t_1} \hat{i}$$

The negative sign means that the force exerted BY the wall ONTO the mass is in the -x direction, i.e. to the left in the figure. The answer options in the question only care about the magnitude. But even so, as you can see, you can't ignore that these are vectors till the very end.

Moral of the story here is that you need to do this very carefully and to follow the "rules" meticulously. Otherwise, you'll get trapped with the signs issue.

Zz.

 

[haruspex]

This is what it looks like visually:

View attachment 236639

Hmmm... i would show it as v with an arrow to the left, or, equivalently if puzzlingly, -v with an arrow to the right.