I am currently learning Newtons Second Law in my physics class. The question tha

Question

I am currently learning Newtons Second Law in my physics class. The question that I am stuck on is regarding a flat plane with a cart on it. The surface is not frictionless and the carts mass is 250 g. There is a string attached to the cart that is being pulled straight down by gravity and it's mass is 50 g. The cart is given an intial veolecity in the opposite direction of the string/weight. At this moment the cart has a high rate of acceleration. At a certain point however the carts direction switches and the cart begins to return back to it's starting position. Durning this time the acceration is lower then when the cart was moving away from the starting point. Why is the case? If the mass of the cart/weight never changed why did the cart experience faster acceration when moving against gravity then it did when gravity was working with it to pull it back to the starting point?

Explanation / Answer

If forget about the masses of the cart and string etc, there are two forces acting on the cart continuously, one its weight mg acting downward and other normal reactions N acting on it due to string or plane on which it is kept or due to any other thing. As the cart is over all moving upward so N should be more than mg, so net upward force is given by F = N - mg, so using Newton's second law of motion, F = ma, hence ma = N - mg

So N = m(g + a)

So net acceleration becomes g + a

On the other hand when cart will be coming down, mg will be more than N, hence now net force F = ma = mg - N

So N = m(g -a), means net acceleration appears to be reduced and becomes g - a.

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