# Work done by force acting on a spring

Doc Al
Interesting that you consider C as doing work now, but didn't before.
While F is acting what work do you consider C doing, since it is the pull of the spring on the mass?

Doc Al
Mentor
While F is acting what work do you consider C doing, since it is the pull of the spring on the mass?
I thought I explained that in my last post. If you want to look at the mass alone, you cannot just consider force F acting. F does positive work, while C does negative work. The net work done on the mass is zero. (Consider the change in energy of the mass alone.)

Now for some reason you have no problem considering C as doing work when the force F is removed. But it was always there, doing work.

We are granted a frictionless surface.

Let the spring be temporarily disconnected from the mass and again apply F in the same slow differential manner so that it moves the mass to s1.

What work has been done?

Doc Al
Mentor
Let the spring be temporarily disconnected from the mass and again apply F in the same slow differential manner so that it moves the mass to s1.
You won't be able to do that, since there will be a net force on the mass now and it will accelerate.
What work has been done?
W = ∫F*dx.

But now the work done by force F will lead to an increase in the kinetic energy of the mass.

Do you think that the change in position of the mass results in a change in its potential energy, because the spring is then extended?

Doc Al
Mentor
Do you think that the change in position of the mass results in a change in its potential energy, because the spring is then extended?
I thought you disconnected the spring.

Sorry if the lines of thought were disconnected.

This is back to the original setup.

Force F is applied to draw back the mass attached to the spring to s1 and

1) Held in position.

2) Then it is released (F is removed)

Do you think the mass has gained potential energy as a result in (1) and (if so) does it still possess this energy at the moment of release of F or just after (2) ?

Doc Al
Mentor
Do you think the mass has gained potential energy as a result in (1) and (if so) does it still possess this energy at the moment of release of F or just after (2) ?
The system has gained spring potential energy. And that potential energy depends only on the amount the spring is stretched from its equilibrium position.

So: Yes, the system has PE when it is held in position (1) and immediately after the force F is removed (2).

As soon as the spring is stretched it exerts a pull on the mass, which will move the mass if we let go.

What is the difference between that pull and the pull on the mass due to gravity, which would draw it down if we removed the table?

Doc Al
Mentor
As soon as the spring is stretched it exerts a pull on the mass, which will move the mass if we let go.
Sure.
What is the difference between that pull and the pull on the mass due to gravity, which would draw it down if we removed the table?
What point are you trying to make? (You're losing me.)

The objective is an energy balance or accounting.

(It's not a trick 'onest guv)

I'm merely observing that we can (I think) say that the mass has potential energy due to the elastic energy stored in the spring and thereofe the pull exerted by the spring.

This is eventually transferred to the mass as kinetic energy when it oscillates and forms the energy of the oscillation ie that which is transferred back and fore between KE and PE.

I want to end up by observing that the force F does work on the mass, which in turn does work on the spring when pulled out so the net energy of the mass does not increase when it has reached a stop at the maximum s1

Doc Al
Mentor
The objective is an energy balance or accounting.

(It's not a trick 'onest guv)

I'm merely observing that we can (I think) say that the mass has potential energy due to the elastic energy stored in the spring and thereofe the pull exerted by the spring.

This is eventually transferred to the mass as kinetic energy when it oscillates and forms the energy of the oscillation ie that which is transferred back and fore between KE and PE.

I want to end up by observing that the force F does work on the mass, which in turn does work on the spring when pulled out so the net energy of the mass does not increase when it has reached a stop at the maximum s1
I prefer to say that the system (really the spring) has potential energy, not just the mass. (For the same reason I think it is misleading to talk about the gravitational PE of a mass--it's really the PE of the mass-earth system.)

The force F does work on the system. The mass essentially transmits the force to the spring, which gets spring PE as it is stretched. When the mass is allowed to oscillate, the spring and mass exchange energy.

I don't see the issue. (Or how it relates to the OP's concern.)

it's really the PE of the mass-earth system.)
Yes that's true enough.