Deriving formula for force by thought experiment

[Boltzman Oscillation]

TL;DR Summary

Was thinking of how I can derive force from a simple thought experiment but I came up with F = md where d is displacement. Why can it not be this?

Hi all, I was thinking punching a round ball on a flat surface and seeing how I could determine a formula for force from it. I thought the following:

1. The ball will go further the harder I punch and thus force must be proportional to displacement d.

2. Ball will go further if it is lighter thus force is inverse proportional to m.

This I came up with F = md. If I experimented I would assume to get the wrong answer since force is F=ma in classical physics. So I came up with the following to challenge the outcome of F=md:

1. displacement does not take into consideration friction.
2. Even if the formula was correct then it would be useless for determining gravity as the ball would eventually be stopped by the ground and if there is no ground and the ball was falling forever then the displacement would be infinite and the force would be infinite. This brings us back to 1 if we see the ground as 100% friction and no ground as 0% friction.

Are there any other ideas I'm missing as to why F != md?

 

[anuttarasammyak]

If you choose not a round ball but spring displacement for your thought experiment, you will be able to get force in proportion to d.

 

[Drakkith]

Are there any other ideas I'm missing as to why F != md?

I feel like you've done this backwards. Instead of asking why ISN'T force proportional to MD, ask why force IS proportional to MD. Otherwise the only real answer you can get is, "That's not how nature works".
This way, if you do find a situation in which f=md, you only have one situation to describe, not an infinite number of examples or explanations of why it doesn't.

 

[jbriggs444]

Are there any other ideas I'm missing as to why F != md?

You are assuming that the strength of the impact of fist on ball is characterized by "force". It is not.

If one multiplies (actually integrates) the force of the impact by the duration of the impact, one can get "impulse" -- the amount of momentum transferred.

If one multiplies (actually integrates) the force of the impact by the distance traversed during the impact, one can get "work" -- the amount of energy transferred.

 

[Boltzman Oscillation]

I feel like you've done this backwards. Instead of asking why ISN'T force proportional to MD, ask why force IS proportional to MD. Otherwise the only real answer you can get is, "That's not how nature works".
This way, if you do find a situation in which f=md, you only have one situation to describe, not an infinite number of examples or explanations of why it doesn't.

Interesting, I should be asking why something is and not isn't in order to reduce the answers. Thank you for the advice!

 

[Boltzman Oscillation]

You are assuming that the strength of the impact of fist on ball is characterized by "force". It is not.

If one multiplies (actually integrates) the force of the impact by the duration of the impact, one can get "impulse" -- the amount of momentum transferred.

If one multiplies (actually integrates) the force of the impact by the distance traversed during the impact, one can get "work" -- the amount of energy transferred.

I'm sorry are you saying that the strength of the impact is not related to force? What do you mean by that? If I hit a ball with more force than someone else did to a similar ball than my ball would go further would it not?

 

[Boltzman Oscillation]

If you choose not a round ball but spring displacement for your thought experiment, you will be able to get force in proportion to d.

Ah, another classic problem. Thank you, I will try to work this one out similarly and see what I can get.

 

[jbriggs444]

I'm sorry are you saying that the strength of the impact is not related to force? What do you mean by that? If I hit a ball with more force than someone else did to a similar ball than my ball would go further would it not?

Not necessarily. It depends on more than just a single number for force.

For a ball projected on a flat surface with kinetic friction, the distance traveled will scale with energy transferred. A fellow applying a small force with a shuffleboard stick can get as much distance as another fellow applying a large force with a hammer.

 

[A.T.]

If I hit a ball with more force than someone else did to a similar ball than my ball would go further would it not?

What matters is the force integrated over the collision duration, not the maximal value of force reached.

 

[PeroK]

If I hit a ball with more force than someone else did to a similar ball than my ball would go further would it not?

It would have a greater acceleration. That's Newton's second law.

 

[PeroK]

Are there any other ideas I'm missing as to why F != md?

Force is a vector:

Explain circular motion, where force and velocity are orthogonal.

Distance is frame dependent. If you hit something that's already moving It may stop.

Without friction or orher retarding forces, the total distance is infinite for any force given as a single impulse.

The units are wrong.

...

 

[anorlunda]

If I hit a ball with more force than someone else did to a similar ball than my ball would go further would it not?

No. Strike a cannonball with a hammer and see how far it goes. The answer is almost nowhere even though the instantaneous force of the strike was large.

Now shoot the cannonball from a cannon. The pressure on the ball acts for the whole time the ball is in the barrel. But the maximum force on the ball may be less than the maximum with the hammer.

As others said, force times time is what counts. Not force alone. If the force varies with time, then force times time becomes the integral of force with respect to time.

 

[Boltzman Oscillation]

Not necessarily. It depends on more than just a single number for force.

For a ball projected on a flat surface with kinetic friction, the distance traveled will scale with energy transferred. A fellow applying a small force with a shuffleboard stick can get as much distance as another fellow applying a large force with a hammer.

I see what you mean. Thank you.