Relative Work - not sure what it means-

[yttuncel]

Homework Statement

Two people push in opposite directions on a block that sits atop a frictionless
surface (The soles of their shoes are glued to the frictionless surface). If the
block, originally at rest at point P, moves to the right without rotating and ends
up at rest at point Q, describe qualitatively how much work is done on the
block by person 1 relative to that done by person 2?

https://docs.google.com/viewer?pid=bl&srcid=ADGEESibEj7pzQOnOXVNPdE4L1V9YvbZjDsvpoIYd9X36QE73jfnjn3DCgrDR-bbW3An133sPXBv0FACZ65q9TpkFy0t6LlDRzoc3OuWYQmxt4BP_ek_7CKff7heIXLJOepSzUmLmkaW&q=cache%3Apu-zuL8y6zkJ%3Aocw.mit.edu%2Fcourses%2Fphysics%2F8-01sc-physics-i-classical-mechanics-fall-2010%2Fwork-and-energy%2FMIT8_01SC_problems11.pdf%20how%20much%20work%20is%20done%20on%20the%20block%20by%20person%201%20relative%20to%20that%20done%20by%20person%202%3F&docid=c21a27004575c8d09fb3d870f827860c&a=bi&pagenumber=1&w=800

Homework Equations

W = F*dx

The Attempt at a Solution

I could not make up my mind with the question, what it asks. I said from the direction of the motion we know F1>F2 and thus W1>W2. And also W1 is positive whereas W2 is negative. But what else should i say? Shall i say total work is W1-W2 or something like that ?

 

[Delphi51]

A strange question! I'm wondering why the motion stops. Does person 2 start pushing harder, to overcome F1 and decelerate the block? Maybe it hits his glued-down shoes.
Anyway, the total work is ultimately zero when the kinetic energy disappears. Before that, all is as you said.

 

[yttuncel]

Can you please express your opinion about the last sentence of the question? What does it imply by saying "by person 1 relative to that by person 2?" I mean it does not ask about total work, but I feel uncomfortable that I think I am not answering properly if I say things only in post 1.
Thanks!

 

[Delphi51]

Everything you say is "relative", since you have no way to calculate any absolute numbers.
I'm just thinking of some qualifiers, like F1 > F1 at some point because the box moves to the the right. One does some work on the box and on two. Two absorbs all that work eventually, some gradually, the last of it when the box hits his foot and loses its kinetic energy.

 

[asteriatic]

I would first clarify the term "relative work" to ensure a common understanding. In this context, it could refer to the work done by one person compared to the other, or the work done on the block relative to its displacement.

Based on the given information, it can be assumed that the forces applied by both people are equal in magnitude but opposite in direction, resulting in a net force of zero. This means that the block is in equilibrium and no net work is done on it.

However, we can still discuss the relative work done by each person. Since the block moves without rotating, we can assume that the forces are applied along the same line of action as the displacement. In this case, the work done by each person can be calculated using the equation W = F*dx, where F is the force applied and dx is the displacement of the block.

Person 1 applies a force in the direction of motion, while Person 2 applies a force in the opposite direction. This means that Person 1 does positive work, while Person 2 does negative work. Therefore, the total work done on the block by Person 1 is greater than that done by Person 2, and the net work done is equal to the difference between the two.

In conclusion, the relative work done by Person 1 is greater than that done by Person 2, and the net work done on the block is equal to the difference between the two. It is important to note that this analysis assumes ideal conditions and does not take into account any external factors that may affect the forces or displacement.