Quick question about spring compression and work

[Gabbo]

This is my first time posting, but I've done quite a bit of reading around on here, and I admire your guys' intuition/skills for this stuff. Most of you appear to have a real knack for conceptualizing these problems, and I'm jealous ;).

Homework Statement

Two identical blocks, A and B, on a frictionless surface are connected by a spring of negligible mass. The spring is initially unstretched. During the interval from t₁ to t₂, block A is pushed through a distance d_A by a hand exerting a force of magnitude F_A, as shown. Block B is held in place by a wall. The wall exerts a force on block B that varies with time but is always directed to the left.

Write an expression for the net external work done on system ABS by external forces in terms of given quantities (ie. F_A, d_A, and/or t₂). Explain.

Homework Equations

Work = Force * displacement

The Attempt at a Solution

The diagram shows block B resting against a wall, and block A being moved toward B, compressing the spring and moving displacement d_A. Block B has zero work done on it (because it experiences no displacement), and block A has work F_A*d_A. So I know that the net work will have at least that component to it.

My question is, do we account for the force of the wall being exerted on block B when we're describing total work on the system? My reasoning is that because the spring experiences compression that wouldn't otherwise occur without the wall, there appears to be a transfer of energy that occurs (that's stored in potential energy of the spring).

This is obviously flawed logic though, because the only parts of the system that are experiencing displacement are the parts being directly influenced by the hand, and therefore they must be the only parts of the system with work being performed on them. Could I get some help straightening this out?

Thanks!

 

[kuruman]

Hi Gabbo, welcome to PF and thanks for your kind words.

Look at it this way. The block that is against the wall experiences two horizontal forces, one from the wall and one from the spring. Because this block does not move (no displacement) there is no work done to it by either of these forces, so there is no transfer of energy to it.

Forces convert energy from one form to another by doing work on objects. So the Joules of work done by the hand on the moving mass get converted to Joules stored as potential energy in the spring and Joules that appear as kinetic energy of the moving mass. The Joules that are stored as potential energy in the spring are also known as the negative of the work done by the spring on the moving mass.

 

[tiny-tim]

Welcome to PF!

Hi Gabbo! Welcome to PF!

Write an expression for the net external work done on system ABS by external forces …
…
The diagram shows block B resting against a wall, and block A being moved toward B, compressing the spring and moving displacement d_A. Block B has zero work done on it (because it experiences no displacement), and block A has work F_A*d_A. So I know that the net work will have at least that component to it.

My question is, do we account for the force of the wall being exerted on block B when we're describing total work on the system? My reasoning is that because the spring experiences compression that wouldn't otherwise occur without the wall, there appears to be a transfer of energy that occurs (that's stored in potential energy of the spring).

You have a rather confused way of looking at work done …

you're considering the work done for each block.

The question asks you for the net work done on system ABS by external forces.

You should go straight to considering the work done for each force, not break it down into blocks.

(if you're worried about where the energy for the spring comes from, remember that that'll be the same in any inertial frame of reference, and the work done by the wall and the hand will gradually "change places" as you gradually change the frame)

 

[Gabbo]

Forces convert energy from one form to another by doing work on objects. So the Joules of work done by the hand on the moving mass get converted to Joules stored as potential energy in the spring and Joules that appear as kinetic energy of the moving mass. The Joules that are stored as potential energy in the spring are also known as the negative of the work done by the spring on the moving mass.

This makes a ton of sense, and explains a lot... It helps a lot to think of the work done on a system by a force as a conversion of energy from one form to another.

(if you're worried about where the energy for the spring comes from, remember that that'll be the same in any inertial frame of reference, and the work done by the wall and the hand will gradually "change places" as you gradually change the frame)

Right; if we take the block to be fixed, then the wall is what's doing the work on the spring instead of the block. The confusion in this whole thing came when I imagined the system without the wall- energy wouldn't be stored in potential energy within the spring, and I didn't realize kinetic energy would account for the work done by the hand >.<.

Thanks a ton for the help!