# Prove that F=ma

1. Oct 6, 2004

### FUPA

I am designing a lab to prove that F=ma. However i am only using a spring scale, 1 kg mass, string. I have come up with a procedure where you would attach the mass to the scale and accelerate the unit upward, recording the time it takes the unit to accelerate from 0-1m and the force shown in the scale. From these measurements i can find the acceleration and than prove that T-ma=mg. However, there is great percent of error as the acceleration by hand proves inconsistent. Is there anyway to get a constant acceleration by hand using the materials listed above?

2. Oct 7, 2004

### Tide

If your measurements are so unreliable why don't you use the weight and string to construct a pendulum instead. You can more accurately measure the period of a pendulum for various lengths and, in the end, the period you calculate derives from Newton's Laws.

By the way, performing a single experiment does not "prove" the theory. You are verifying that it is consistent with your particular experiment.

3. Oct 7, 2004

### Chronos

Are you factoring gravitational acceleration into your experiment?

4. Oct 7, 2004

### maverick280857

Well one of the things we did back in school to "prove F = ma" (actually it was more like "verify F = ma" because a proof is not possible using one case and revolving a theory around it) was the pendulum experiment. It is not possible to use an experiment to prove something in the pure form because in such an experiment, nonidealities will creep in and will distort your readings so if you use F = ma to check them, I'd believe it won't give you the same readings as your experiment. So the simplest way to do this, as Tide has suggested is the pendulum experiment.

F = ma was not mathematically proved from first principles, as are theorems of mathematics. It was based on experimental wisdom and conclusions. Newton's Laws are emperical relationships. They can be verified not proved this way.

Cheers
Vivek

5. Oct 7, 2004

### FUPA

Pendulum experiment? How would I verify its relation to F=ma mathmatically? I assume we are using P=2Pi sqrt(l/g). Recording the length and period?

Last edited: Oct 7, 2004
6. Oct 7, 2004

### Tide

There would be two steps. First you would "predict" the period using Newton's laws (F = ma) by resolving the components of the force. The formula for the dependence of the period on the length of the pendulum follows from that. You would then measure the period for various lengths thus verifying the dependence and the original postulate (F = ma).

7. Oct 7, 2004

### Pyrrhus

Yes, indeed a simple pendulum can prove $\vec{F} = m\vec{a}$, and also it can be useful to learn Simple Harmonic Movement

8. Oct 10, 2004

### maverick280857

It can also be useful to have some fun (after all Physics is fun isn't it).

9. Oct 10, 2004

### PrudensOptimus

I do not think you can prove F = ma, because F is not ma... It is only ma when the object remains constant mass under all circumstances of the forces. And obviously traveling at highspeed is an exception.

F is dp/dt...

10. Oct 11, 2004

### Pyrrhus

Yes, but he did refer to a constant mass.

11. Oct 11, 2004

### maverick280857

Yes it was meant to be a school/college laboratory experiment (a starter). You can't have high speed motion and variable mass all in one bucket in a simple experiment; though your experimental readings in the simple pendulum experiment will be corrupted by non-inertial effects of the earth, air resistance and non-uniformity of the bob/string, nonzero mass of the string etc. You cannot possibly account for all of those without making further errors (you might for instance want to add a drag term to the left hand side of your differential equation but you'll be making an error in chosing the right drag term anyway!).