# Need help with designing an experiment to prove that F=ma

1. Jul 6, 2004

### oranges and lemons

Anyone know a simple and non-complicated experiment that I can do to prove this law?

2. Jul 6, 2004

### Integral

Staff Emeritus
The goal would be to apply a constant force to a body then measure the resulting acceleration. This sounds pretty easy, but is not necessarily so.

The first thing you will need is some form of a frictionless (read low friction!) table (Air hockey?).

A common method of applying a constant force is to use a spring and pull the body along maintaining a constant LENGTH of the stretched spring. This takes some practice.

So you place your experimental mass (the Body) on the frictionless surface and pull it along with the spring as described above. Now you need to measure the acceleration.

This is best done by recording the position at regular time intervals as the Body moves along. This can be tricky and may require some instrumentation. Perhaps the biggest challenge will be a repeatable measure of your acceleration, there exist modern instrumentation which can do it easily but this stuff is not free.

What ever you choose to do, repeat it many times. Since human error is a large factor in this type of experiment, the more times you run it, the more data you gather the more meaningful your results.

3. Jul 6, 2004

### oranges and lemons

A common method of applying a constant force is to use a spring and pull the body along maintaining a constant LENGTH of the stretched spring. This takes some practice.

I don't get this bit. Oh and how do I measure the amount of force I used?

4. Jul 6, 2004

### Integral

Staff Emeritus
The force on spring is given by Hooks law.

F=-kx where k is the spring constant and x is the displacement from the equilibrium position of the spring.

So... Hang a mass from the spring to gently stretch it, then place small, constant increments of mass on the spring. Measure the resulting displacement. If you graph, x vs m the slope of the line will be k. With this knowledge you can calculate the force for a given spring length.

5. Jul 7, 2004

### JohnDubYa

what about simply dropping a rock and measuring its motion to determine the acceleration? It doesn't get much simpler than that.

what I would do is go through a physics textbook and look at all the word problems involving force summation. Re-write the problem so that the acceleration is the unknown, and transform the result into an experiment.

6. Jul 7, 2004

### Integral

Staff Emeritus
You might also read up on Galileo's experiments with rolling balls down a ramp. What this does not give you is a feel for what a constant force is or the relationship between mass and acceleration.

BTW: It is very difficult to maintain the constant force by pulling on a spring.

7. Jul 7, 2004

### gerben

Force is in a way defined by stating that it is equal to mass times acceleration. The usefulness of the definition (F=ma) comes from the fact that it is also defined in other terms, like how a mass exerts a force on another mass (F=G*m1*m2/distance_between_m1_and_m2^2) or how the force depends on the electrical charges of particles. Because of that one can calculated how masses move or how charged particles move.

In Integral's proposal you see how the force that a spring exerts depends on how far it is stretched (F=-k*Stretch_length), that can be used to calculate how it makes some mass that is attached to it move. But note that the force changes when the mass moves because the movement changes the stretch length, so you will need calculus to calculate how the mass will move.

To show that F=ma you will first have to define what you mean with a force and than show that that when you increase the force that than the acceleration increases with the same factor if you do not change the mass. You can also show that when you double the mass de acceleration halves.

You can use a spring, but as Integral said it is no so easy to have it exert a constant force, if you drag an object attached to a spring along and make sure the spring does not stretch more and also does not stretch less the force on the object will be constant and it will accelerate (so you will have to walk faster and faster to keep the stretch length constant), you will then have to find a method to measure the acceleration. After you have done this you repeat it while you try to hold the spring’s stretch length at a different length (the length ratio is equal to the ratio between the forces, as you can deduce from F=-k*Stretch_length).

Last edited: Jul 7, 2004