# Experiment to show $a \propto F$

I learnt about an experiment to show that acceleration is proportional to force. It was done by placing a trolley (like a toy car) on a smooth track. At the end of the smooth horizontal track was a pulley connected to the trolley by a string which hung masses over the edge of the table. So the trolley experienced acceleration due to the weight from the masses.

My problem is in what my textbook says to do next. They say you have to take a mass being hung over the edge, which results in less force applied to the trolley. But then they tell you to put the mass onto the trolley, to ensure constant mass in the system.

The problem is in placing the mass onto the trolley. Surely the trolley's mass should stay constant throughout, since that is what we are measuring the acceleration, and not the system as a whole?

I hope you can explain this to me, or if my book is incorrect. I'll expand on the experiment if you find my description confusing.

One easy way to check that you must add the masses of the trolley and the hung masses is to consider what would happen if you make the mass of the trolley near to 0, that is, almost no trolley at all. If you don't count the mass of the hung masses, the acceleration would go to infinity! But surely the total acceleration would never be over $g$ (gravity).