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Andrew Mason
Jan6-12, 03:19 PM
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Quote Quote by titaniumpen View Post
As far as I know, you can't prove laws, but anyway...

We got to do an experiment at school. A weight is suspended vertically from a string which is connected to a trolley which is placed horizontally on a flat table. There's a pulley at the edge of the table to reduce friction. Then we let the weight fall due to gravity and pull the trolley across the table. The trolley pulls along a tape as it moves, and the tape has to go through a ticker timer, which automatically dots the tape every 0.2 second.

The set up looks like this:

Anyway, we studied the tape and tried to measure the acceleration. We know the force exerted by the falling weight, and we also know the acceleration of the trolley from the tape. We also know the mass of the trolley. So if we put the values into F=ma, which is Newton's Second Law of Motion, we should find that both sides of the equation is the same. Which proves that Newton's Second Law is true!

Now, I don't think you can prove the Second Law like that. How do we know the force exerted by the falling weight on the trolley? The force is mg, right? (m=mass of weight, g=9.81m/s^2) But that is determined using Newton's Second Law. We cannot prove a law by using the law itself. Isn't that a circular argument?

Thanks for reading, this got me thinking for some time...
Getting back to the original post here, what you are trying to do is not to prove Newton's second law in the mathematical sense but to merely verify it - to show that it gives a correct prediction of what happens in nature.

This experiment is sometimes used in high school physics to demonstrate the second law, but it has a particular flaw: the tension force on the string pulling the trolley varies not only with the mass of the falling weight but also with mass of the trolley. What you need is the same constant pull on the trolley for different trolley masses. You would need to pull the car with elastics or springs stretched a set amount.

If you do that, you can show that the acceleration is proportional to the number of springs or elastics and inversely proportional to the mass of the trolley, just as the second law predicts. That demonstrates that Newton's second law provides the correct result. And you will not have used Newton's second law in order to produce your data.