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.

 

[rwisz]

of the weights.

As a scientist, it is important to understand and follow the guidelines and restrictions set for an experiment. In this case, the restriction of not being able to directly use the formula F=ma may seem challenging, but it allows for a deeper understanding and application of the concepts involved.

Firstly, let's consider the setup of the experiment. The cart is being pulled by falling weights, which means that a force is being applied to the cart. This force is causing the cart to accelerate, which means that there is a change in its velocity over time. This change in velocity can be measured and compared to the force applied, which brings us to the concept of acceleration.

Acceleration is defined as the rate of change of velocity, and it is directly proportional to the force applied. In this case, as the weights fall and apply a force to the cart, the cart will accelerate in the direction of the force. This acceleration will be directly proportional to the force applied, meaning that the greater the force, the greater the acceleration.

Now, let's consider Newton's first law. It states that an object will remain at rest or in motion with a constant velocity unless acted upon by a net force. In this experiment, the cart is initially at rest and is then pulled by the falling weights, resulting in a net force acting on the cart. This net force causes the cart to accelerate, which aligns with Newton's first law.

Furthermore, we can also consider the concept of inertia, which is the tendency of an object to resist changes in its state of motion. In this experiment, the cart has an initial state of rest and the weights are causing a change in its state of motion. This change in motion is directly proportional to the force applied, as explained earlier.

In conclusion, through the application of Newton's first law, the concept of acceleration, and the understanding of inertia, we can predict that the acceleration of the cart will be directly proportional to the force of the falling weights. This aligns with Newton's second law, which states that the acceleration of an object is directly proportional to the net force acting on it.