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

• AbhinavJ
In summary, the conversation is about finding the reading on a spring balance in a system where a force F=mg is applied on block C and all pulleys are frictionless. The equation F=ma is used to calculate the acceleration of block B and C. The tension in the spring is found by equating it to the tension in the wire connecting block B and C. It is determined that the reading on the spring balance is equal to (5/2)mg.
AbhinavJ

## Homework Statement

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.

F=ma

## 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.

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AbhinavJ said:
2Twire=Tspring?
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.

haruspex said:
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.
But isn't the pulley accelerating downwards due to the tension in the wire being more than that in spring?

AbhinavJ said:
But isn't the pulley accelerating downwards due to the tension in the wire being more than that in spring?
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?

AbhinavJ
haruspex said:
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.

Got it, thanks :D

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

conscience said:
Is the reading in spring balance = (5/2)mg ?
From memory, that's not what I got, but it is in the ballpark.

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

In that case , I think I have misunderstood the setup .
AbhinavJ said:
A force F= mg is applied on C

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 ?

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conscience said:
Is the reading in spring balance = (5/2)mg ?
Actually that is the answer, the spring balance shows a reading of 5 kg and and m=2kg, thereby 5mg/2 is correct.

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

## 1. What are Newton's laws of motion?

Newton's laws of motion are a set of three laws that describe the relationship between the forces acting on an object and its motion. These laws were developed by Sir Isaac Newton in the 17th century and are still used today to understand and predict the behavior of objects in motion.

## 2. What is the first law of motion?

The first law of motion, also known as the law of inertia, states that an object at rest will remain at rest and an object in motion will continue moving in a straight line at a constant speed unless acted upon by an external force.

## 3. What is the second law of motion?

The second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This can be expressed mathematically as F=ma, where F is force, m is mass, and a is acceleration.

## 4. How do Newton's laws apply to masses on pulleys?

In the case of masses on pulleys, Newton's laws can be used to understand the motion of the masses and the tension in the ropes. The first law explains why an object will remain at rest or continue moving at a constant speed unless acted upon by an external force. The second law can be used to calculate the acceleration of the masses based on the net force and their masses. The third law states that for every action, there is an equal and opposite reaction, which can be seen in the tension forces in the ropes.

## 5. What is the third law of motion?

The third law of motion, also known as the law of action and reaction, states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal and opposite force back on the first object. This can be seen in the example of masses on pulleys, where the tension in the ropes pulling the masses is equal and opposite for each mass.

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