Second law question(Ap Physics)?

Question

Two blocks of masses M and m, with M > m, are connected by a light string. The string passes over a frictionless pulley of negligible mass so that the blocks hang vertically. The blocks are then released from rest. What is the acceleration fo the block of mass M?


Please help!

Answer 1

The total force on the system is F=(M-m)g where g = 9.8 ,/s^2
However, it is M+m that needs to be moved, so
a = F/(M+m) or (M-m)g/(M+m), and this acceleration is downward since M > m

Answer 2

The first thing to realize is that because the blocks are tied together by a string, they have related accelerations - the acceleration of one block is the negative of the acceleration of the other. We'll call the magnitude of that acceleration As and assume that it is downward for the big block, therefore upward for the small one.

Now draw free body diagrams for the two blocks:
(big): -M *g + T = - M As
(small) -m *g + T = m As
Two equations, two unknowns. The question doesn't ask about T, so subtract (1) from (2) to eliminate T and get:

(M-m) g = (m+M) As
As = g (M-m)/(M+m)

If we had assumed the incorrect sign for As, it would be evident here, but since it is stated that M>m, we see that we guessed the correct sign.

Answer 3

I think Marbledog is close, but you have to remember that the two blocks are behaving as one since the string remains in tension. The tension in the string pulling the heavy block M up is not just m*g, since that would be the static tension in the string if the small block m was not accelerating. The small block m IS accelerating, so additional tension is in the string to supply this acceleration.

Try this: a = (9.81*M - 9.81*m) / (M + m)

Answer 4

The net force on the pair of blocks is the difference between their weights.
Fnet = WM - wm = M*g - m*g = (M-m)*g

The net force acts to accelerate the 2 blocks according to Newton's 2nd.
Fnet = (M+m)*a so
a = (M-m)*g / (M+m)

Answer 5

The acceleration will always be the gravity acceleration. 9.8m/sec
The two masses are tied together and if friction is negligible then the two bodies act as a single object, subject to gravity.
Gravity acceleration is independent from the mass.
Force is another story, but they ask for the acceleration only.

Answer 6

Expressed in meters per second squared,
a = (9.81M - 9.81m) / M

Acceleration = force / mass, so the acceleration of the big block is equal to the the sum of the upwards and downwards forces it experiences divided by it's own mass.

EDIT:
You guys are right. a = (9.81M - 9.81m) / (M-m) is correct. Thanks for explaining it.