Acceleration of a cart being pulled by falling weights

[rollcast]

Homework Statement

For my physics practical I have to conduct an experiment where I have to investigate the acceleration of a small cart, its a block of wood with wheels on it.

The set up is I have a one metre distance marked on a desk from the edge of the desk. at the edge of the desk is a pulley wheel. The cart is placed at the start of the metre distance and then tied to a piece of string which goes over the pulley and then connects to weights which pull the cart towards the pulley.

The problem is we have to basically at the end of the experiment show how this is relevant to the formula, f=ma, and therefore Newtons second law, without stating it.

However we have to predict whether that acceleration of the cart will be proportional to the force of the weights or whether it will be directly proportional to the force. I can obviously tell it shall be directly proportional from my knowledge of Newtons second law. However I can't figure out how to explain my prediction without using this law?

He told us that we could and had to use Newtons first law to back this up and also some other general physics as well.

Homework Equations

F=ma, but I can't use it.

The Attempt at a Solution

The closest I have came to explaining is that if Newtons first law states that an object will remain at rest or constant speed as long as no resultant force acts upon it, then the weights are a resultant force which will cause the cart to change from being at rest to a state of motion and that this motion shall be accelerating as the resultant force will still be acting upon the cart.

However that doesn't explain how the acceleration will be directly proportional to the force

 

[AC130Nav]

Why can't you use F=ma? The weight exerts a force at the pulley equal to F=mg (where g is the a due to gravity), and the cart accelerates at a = F/m (same F, without considering friction).

 

[rollcast]

We can't use f=ma as a later part of our coursework is to show how we could use our results to prove Newtons Second law, I know its well proven but its just something we have to do.

So therefore we can't use it as part of our prediction.

 

[AC130Nav]

We can't use f=ma as a later part of our coursework is to show how we could use our results to prove Newtons Second law, I know its well proven but its just something we have to do.

So therefore we can't use it as part of our prediction.

Newton might have thought things in this order: mass is a very old concept (albeit as weight); acceleration is a newer concept related to speed; force is ill-defined but must be related to the other two in such an experiment as you describe. The experiment proves the relationship.