# Newton's laws of motion -- masses on pulleys...

1. Apr 22, 2016

### AbhinavJ

1. The problem statement, all variables and given/known data

A force F= mg is applied on C, all pullies are frictionless and we need to find the reading of the spring balance, basically the tension in it.
2. Relevant equations
F=ma

3. The attempt at a solution
I assumed the pulley and block A are moving downwards with an acceleration a1, then used pseudo forces to calculate acceleration of B and C which comes out to be
g/2. Then I used the equation for A Tspring
- 2mg=2ma1.
I need another equation relating tension in spring to that in wire connecting B and C.
2Twire=Tspring?
Or i can consider the mass of pulley as that of the blocks combined which gives me 2Twire - Tspring=2ma1? The pulley is massless, though.

Last edited by a moderator: Apr 22, 2016
2. Apr 22, 2016

### haruspex

i
Yes. The free body diagram for the pulley only has the massless pulley, the connection to the spring, and the wire running over it. It does not "know" anything about the blocks below.

3. Apr 23, 2016

### AbhinavJ

But isnt the pulley accelerating downwards due to the tension in the wire being more than that in spring?

4. Apr 23, 2016

### haruspex

You are asked to find the reading on the spring,which implies it is a constant reading. That means the spring has reached a constant extension. If the spring balance has negligible mass, what does that tell you about the relationship between the tension above the spring and the tension below it?

5. Apr 23, 2016

### AbhinavJ

Got it, thanks :D

6. Apr 23, 2016

### conscience

Is the reading in spring balance = (5/2)mg ?

7. Apr 23, 2016

### haruspex

From memory, that's not what I got, but it is in the ballpark.

8. Apr 23, 2016

### conscience

In that case , I think I have misunderstood the setup .
I took the above statement as if a constant force F=mg is acting on block C .

If no external force acts on any block and the system is initially at rest , then none of the blocks should move .

@AbhinavJ , could you post the complete problem statement ?

Last edited: Apr 23, 2016
9. Apr 23, 2016

### AbhinavJ

Actually that is the answer, the spring balance shows a reading of 5 kg and and m=2kg, thereby 5mg/2 is correct.

10. Apr 23, 2016

### haruspex

Edit:
I found my previous scribbles and confirm your answer. Sorry, I must have been thinking of a different pulley problem I replied to recently.... the answer there had 8/3 in it.