# MV or 1/2MV^2

1. ### mtworkowski@o

213
My experience is that because a lighter bowling ball can be thrown faster, the force that the ball has is altered. Should I use MV or 1/2MV^2?

2. ### Defennder

2,616
Neither. Force is not described by 1/2mv^2 or mv.

3. ### nicksauce

1,275
Can you maybe clarify your question? Neither MV nor 1/2MV^2 represents a force in any way.

4. ### razored

171
MV = P which is Momentum.
Ke = 1/2 mv^2 which is Kinetic Energy which can be exchanged for Potential energy.

Force is typically defined as , F=ma.

5. ### mtworkowski@o

213
Yes. In the context of trying to deliver energy to the pins, I'm thinking M and V are trade offs as far as energy is concerned. A heavier ball at slower speed or a somewhat lighter ball at higher V.

6. ### pmb_phy

The correct definition of force is F = dp/dt.

Pete

7. ### xArcherx

35
Just though I would throw in the more accurate formula for momentum (or so it seems)...

p = ɣmv
ɣ = (1-v^2/c^2)^(-1/2)

8. ### mtworkowski@o

213
I'm getting the dp/dt thing from calc 1 97 years ago. thank you Pete. But I missed the thing from xArcherX. Sorry. I'm rusty as hell. Break it down, as they say, please. thanks.

Last edited: Jun 28, 2008
9. ### Gear300

xArcherx's perspective is essentially the same as what you've been learning, but in general form. In classical physics, we mostly deal with what we can experience, which is one of the things that makes modern physics different (it tells us we've only been seeing part of the picture, and that phenomenon start acting differently over different scales).

If you've noticed, there is a c in the equations, which is the speed of light. Compared to v (the velocity of the bowling ball), its probably much bigger, so the formula for momentum can more or less be regarded as p = mv for this situation with the bowling ball.

17,336
Staff Emeritus
Why would you do that? It adds a totally unnecessary complication for no good reason other than to make you look smart. (And I'm afraid adding totally unnecessary complications doesn't make one look very smart)

A bowling ball might travel at 20 mph. That means we are talking about a correction in the 15th decimal place. Not only is this totally unmeasurable, it's tiny compared to the correction to the mass of the bowling ball as it travels and picks up and drops off various bits of this and that. So not only is it an unmeasurable correction, it's not even the biggest unmeasurable correction.

11. ### mtworkowski@o

213
But when looking at a trade off between speed and weight, we use MV and not 1/2MV^2?

12. ### cristo

8,394
Staff Emeritus
What are you actually trying to calculate? It would be a lot easier if we had a well-defined problem.

Note that the two things you have formulae for are momentum and kinetic energy, respectively.

13. ### mtworkowski@o

213
which is better, the 16lb ball or a 15. More detail, if I or anybody can throw a 16 lb ball at the pins and deliver a certain amount of energy(let's say thats as fast as he can comfortably throw the ball) than would a lighter ball ( assuming he can throw it a wee bit faster) deliver more energy. I don't know if its momentum, kinetic energy or if either one will work.

Last edited: Jun 28, 2008

### Staff: Mentor

Firstly, it is both conservation of momentum and conservation of energy that dictate what happens. I good starting point is to assume perfectly elastic collisions. Together, conservation of momentum and conservation of energy tell what happens.

Secondly, your physiology rather than physics is the determining factor here. You are missing a key factor, which is throwing a ball accurately. Suppose that you can throw a 16 lb ball fast enough to get more pin action than you can get with a 15 lb ball. That does not necessarily mean you should prefer the heavier ball. If the heavier ball makes you less accurate you might want to use the lighter ball.

15. ### mtworkowski@o

213
Thanks DH..........I did better with the 15. But this is more of an academic question I guess. Compare the energy delivery of both balls when an equal force is used in each case. Maybe that says it better. Sorry.

16. ### xArcherx

35
Yeah it is pretty much unnecessary at speeds that are not relativistic. Although, personally, I like to work with as close to exacts as I can. I also like to try and look smart , even if it does backfire on me (something that happens way too often):tongue:

17. ### mtworkowski@o

213
to all. you know my question is perfectly clear. If you can't answer it than i'm out. you can just debate it for the next thousand years, which i'm sure you will. By The idea of using relativistic physics on a bowling bowl. Ha Ha Hal. What a joke.

18. ### gamesguru

85
If we assume that you want to accelerate each bowling ball to the same speed, because you only have one swing to do it and want the same final speed, then you can assume,
$$F\propto m$$.
Here's why.
$$\frac{1}{2}mv^2=W=\int_0^d ma dx=ma\int_0^d dx=mad$$
So...
$$\frac{1}{2}mv^2=Fd$$
and finally,
$$F=\frac{1}{2d}mv^2$$
with d and v constants,
$$F\propto m$$.

19. ### Janus

2,367
Staff Emeritus
Assuming that you use the same length swing, and are able to exert the same force throughout the swing, then the energy delivered to the ball is found by

$$E= fd$$

IOW, the ball will deliver the same energy regardless of its mass.

20. ### mtworkowski@o

213
So are you saying it's a one to one trade off between mass and velocity? So I don't use 1/2MV^2. That was my original question, I think.