Question

Consider the situation shown in the picture. Both of the pulleys and the string are light and all the surfaces are frictionless. (a)Find the acceleration of mass M. (b)Find the tension in the string.

Answer 1

Acc. of the mass 2M will be a/2 if the acc. of the mass M is a since the distance covered by the mass 2M is half of the distance covered by the mass M in a given time t. But how to show it??

Answer 2

@Vincent-Lyon.Fr

Answer 3

@rajat97

Answer 4

To prove this, we usually use velocities. Allow me 2 minutes.

Answer 5

sure

Answer 6

Bottom string is fixed.
Top string is moving with speed v1

Answer 7

I find a = (2/3)g

Answer 8

right answer

Answer 9

what are v(a) and v(b)?? I didn't get

Answer 10

v(A) is speed of point A (belonging to string or to pulley)
v(B) is speed of point B (belonging to string or tu pulley)

v(C) is speed of centre of pulley.

Answer 11

why v(A) is zero?? and v(b) not??

Answer 12

Because A belongs to bottom part of the string. This part is fixed at one end and inextensible, so all points belonging to this part have the same speed : zero.

B belongs to top end of the string, attached to mass M. Since string is inextensible M ans B have the same speed (I called it v1).

Answer 13

ohhk, got it..but why v(C) = w.R ?? and v(B)=w.2R?

Answer 14

Because, as v(A) = 0 , A is axis of rotation of the pulley.
C is at distance R of centre of rotation, hence v = R.w
B is at distance 2R of centre of rotation, hence v = 2R.w

Answer 15

@Vincent-Lyon.Fr you are great.
thank you so much.

Answer 16

yw :)

Answer 17

Have you seen this question?

For the same reason I mentioned above, you can say the plank is twice as fast as the centres of the wheels.
http://openstudy.com/users/wach#/updates/52b6534fe4b02932bbc06c03

Answer 18

yeah...right. I need to learn concepts of rotational mechanics. BTW i'm posting one more problem. I'll need your help. I'll give you steps and equations, you will tell where i'm wrong.