Accelerating motion with a pulley

[House]

Let's suppose we have a body A with mass M that can move on a horizontal frictionless ground. Now we connect that with another body B, mass m, with the help of a rope. The body B can move vertically and the rope is curved with a pulley. Now we set the body B free to move.
What's the relationship of the motion of the two bodies? Is there a same force (tension_A = weight_B or a same acceleration?

 

[Dr.D]

The usual approach to this sort of problem involves three assumptions:
1) the rope is inextensible (it does not stretch)
2) the pulley is massless
3) the rope is massless
None of these is ever strictly true, but they significantly simplify the problem. Are you willing to live with these assumptions, or if not, what do you wish to assume instead about these two matter?

 

[A.T.]

tension_A = weight_B

If the tension would be equal to the weight of B, then B wouldn't start falling.

 

[House]

The usual approach to this sort of problem involves three assumptions:
1) the rope is inextensible (it does not stretch)
2) the pulley is massless
3) the rope is massless
None of these is ever strictly true, but they significantly simplify the problem. Are you willing to live with these assumptions, or if not, what do you wish to assume instead about these two matter?

Absolutely, I just forgot to mention them.

 

[Dr.D]

You need to draw FBDs for each body, and do not assume that T = Wb. Also, look at the kinematic constraint imposed by the inextensible cord.

 

[House]

Okay, so a professor of mine told me that the rope carries the same force from B to A. But same force means different acceleretion if the masses are different. If this is true how can different parts of the rope have different acceleretions if the rope is inextensible?

 

[jbriggs444]

Okay, so a professor of mine told me that the rope carries the same force from B to A. But same force means different acceleretion if the masses are different. If this is true how can different parts of the rope have different acceleretions if the rope is inextensible?

The same net force means the same acceleration. What forces act on object A? What forces act on object B?

 

[Dr.D]

I repeat, you need to draw the FBDs for the two blocks. When you do, if done correctly, it will all become clear to you.

 

[Dale]

@House I agree completely with @Dr.D on this. Draw the free body diagram

 

[House]

So, according to the FBDs we have a force for each object, but again I can't decide if the tension is the same as the weight or the accelerations are the same. I'm completely stuck here.

 

[House]

Update: Problem solved. Thanks a lot for your time, much appreciated.