# Extension of spring pulled at both ends

• terryds

## Homework Statement

A spring with spring constant 50 N/m is pulled with 10 N force at both ends of the spring.
So, the extension of spring length is..
A. 0.0 m
B. 0.1 m
C. 0.2 m
D. 0.3 m
E. 0.4 m

F = k Δx

## The Attempt at a Solution

F = 10 N <--- 0000000000000000000000 ----> F = 10 N

I think the Δx should be 20/50 = 0.4 m

But, the teacher said that it should be 0.2 m.
He said that it's like a common problem where the spring is attached to the wall, and we pull it.
The wall exerts the reaction force which magnitude is the same as the pulling force, but in opposite direction (reaction force).

But, then I think, if the reaction force given by the wall is the same magnitude as the action, the spring won't get stretched, right?
I think the reaction force must be less than the one I exert on the spring..

I somehow don't get the insight.

## Homework Statement

A spring with spring constant 50 N/m is pulled with 10 N force at both ends of the spring.
So, the extension of spring length is..
A. 0.0 m
B. 0.1 m
C. 0.2 m
D. 0.3 m
E. 0.4 m

F = k Δx

## The Attempt at a Solution

F = 10 N <--- 0000000000000000000000 ----> F = 10 N

I think the Δx should be 20/50 = 0.4 m

But, the teacher said that it should be 0.2 m.
He said that it's like a common problem where the spring is attached to the wall, and we pull it.
The wall exerts the reaction force which magnitude is the same as the pulling force, but in opposite direction (reaction force).

But, then I think, if the reaction force given by the wall is the same magnitude as the action, the spring won't get stretched, right?
The force is the same in magnitude but opposite in direction. That makes all the difference ...

• SammyS
The force is the same in magnitude but opposite in direction. That makes all the difference ...

So, you agree that the extension is 0.2 m ??

So, if the spring is attached to wall and then get pulled out, the wall gives a reaction which magnitude is the same as the pull force??

How come the spring get stretched if the net force working on it is zero?
Or, does it mean the spring get double-stretched since the force pulls both ends of the spring??
Please explain me the concept ._.

So, you agree that the extension is 0.2 m ??

So, if the spring is attached to wall and then get pulled out, the wall gives a reaction which magnitude is the same as the pull force??

How come the spring get stretched if the net force working on it is zero?
The net force on the spring is not zero. Force has magnitude AND DIRECTION. Force is pulling equally on both ends or it would accelerate per F = ma.
Or, does it mean the spring get double-stretched since the force pulls both ends of the spring??
.
This is a matter of definition. We say the spring constant is the force applied equal in magnitude but opposite in direction divided by the stretch of the spring.

The net force on the spring is not zero. Force has magnitude AND DIRECTION. Force is pulling equally on both ends or it would accelerate per F = ma.This is a matter of definition. We say the spring constant is the force applied equal in magnitude but opposite in direction divided by the stretch of the spring.

Why the net force is not zero?? I know the force has direction too -_-
The Free Body Diagram for the spring is like this, right?

(Assume 000000000 is a spring figure hahaha)

10 N (the reaction force) <-------- 0000000000000 -------> 10 N (The pulling force)

Because the direction is opposite, so the force cancels out, so net force is zero... So, the extension is zero

But, we can also make separate Free Body Diagram for both ends

000 -------> 10 N

Which means that the extension is 0.2 m at one end

10 N <-----000

That means the extension is 0.2 at the other end.
So, the extension is 0.2 + 0.2 = 0.4 m

Why the net force is not zero?? I know the force has direction too -_-
The Free Body Diagram for the spring is like this, right?

(Assume 000000000 is a spring figure hahaha)

10 N (the reaction force) <-------- 0000000000000 -------> 10 N (The pulling force)

Because the direction is opposite, so the force cancels out, so net force is zero... So, the extension is zero

But, we can also make separate Free Body Diagram for both ends

000 -------> 10 N

Which means that the extension is 0.2 m at one end

10 N <-----000

That means the extension is 0.2 at the other end.
So, the extension is 0.2 + 0.2 = 0.4 m

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