Total mass of system and Force In physics class we did an experiment where we pulled a trolley (with weights) with a mass to show $F=ma$. The mass was dangling off the table and thus the force of acceleration was gravity. The diagram below resembles the setup (but there were weights on the trolley and there was a ticker timer behind it)

However, the main issue I'm having understanding is that we always took mass off the cart to put onto the hanging mass. This confuses me for several reasons. It seems like we are changing 2 variables - both the force pulling the cart but also the weight of the cart which affect the force needed to pull it.
As we increase the mass of the hanging mass the force will increase given by $F=ma$ as a of gravity is constant. The force required to move the trolley will also decrease with decreased weight no?
I heard an explanation involving how the total system mass needs to stay constant but I wasn't able to catch on in class.
 A: *

*Removing mass from the cart causes higher acceleration, yes. This is Newton's 2nd law.

*Adding mass to the hanging block increases the weight, which in turn increases the string tension that pulls that cart, which also causes higher acceleration.


Both of these effects happen when you move mass from the cart to the hanging block. Moving a mass thus gives the same effect as adding two masses (assuming no friction). And exactly how big the effect is, is not important in your demonstration here - you just need to show that the acceleration increases proportionally to the force, whatever that force is changed to.
But if you add two masses, then you are changing the mass of the whole setup. When you want to demonstrate Newton's 2nd law, $\sum F=ma$, then you want to vary the force for a constant mass and see that the acceleration grows proportionally. If you add more mass, then you haven't shown this.

As we increase the mass of the hanging mass the force will increase given by F=ma as a of gravity is constant. The force required to move the trolley will also decrease with decreased weight no?

Yep, this is true (just say mass of the trolley instead of weight, since the trolley's weight doesn't matter). And what you have explained here is no issue. You are just pointing out a "reconfiguration" within the system that doesn't matter to what you wish to show.

I heard an explanation involving how the total system mass needs to stay constant but I wasn't able to catch on in class.

Your teacher is considering cart-and-hanging-block as one system, and surely Newton's 2nd law should hold true on this system (it always holds true, for individual parts, for the whole system etc.).
So moving mass from one to the other internally inside the system does not change the system's total mass. But it does change the force on the system, and the acceleration can be easily measured with you ticker timer. So this is a goo method for a Newton's 2nd law demonstration.
