Physics Questions????

Question

I think i have the answers, but i am not sure about the method. Can you check these and tell me why i am right?

1) A force accelerates a body of mass M. The same force applied to a second body produces three times the acceleration. What is the mass of the second body?
My friend tells me the answer is M/3 and i don't understand why.

2) A mass m is hanging on a string that passes over a pulley and is then attached to another mass 3m that is resting on a horizontal table. Neglect friction. Mass m is held motionless and is then released. When it has fallen a distance h, it will have a speed v. Find the formula for v.
On this one, i get the squareroot(gh/2), but as i am following my work, parts of it don't make sense to me. Can you show me if this is correct or not?

This is it for now, thanks so much!!!!!

Answer 1

I'm not sure why nobody has answered this.

1) You know f-ma, right? Two forces are equal so use m1*a1 = m2*a2. The two masses are M and X (the unknown mass) and the two accelerations are a and 3a.
So Ma = X(3a)
Then X = Ma/3a = M/3
This is like story problems in math.

2) Have you stated the problem wrong? If m is released and 3m is the one sitting on the table, it won't move. If you really mean m is on the table and 3m gets released, the downward force due to gravity is 3mg, and the upward force due to the other mass is mg, so the net downward force is 2mg. This causes acceleration of a=F/m = 2mg/m = 2g

For distance h, velocity v, and time t (constant acceleration, v=h=0 at time t=0):
v = at
h = at^2/2
(If you have calculus background, v is the derivative of h, and a is the derivative of v)

To get v in terms of h, solve second for t:
t = square root of (2h/a)
Then v = at = a * sq root of (2h/a) = sq root of (2ah)
Since a = 2g, then v = sq root of (4gh)

Do you see your mistake? (Or did I mess up? I double checked it)