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# Physics/Work

Question
i hope i m not bothering the site by repeatedly posting the questions, but i guess my conceptual doubt list had skyrocketed and had to do something to get it down...
anyways, my question is as stated by the work energy theorem, work done on a body is the change in kinetic energy of that body, so when we push any stationary object, we did some positive work on it and as a result some thermal energy will be produced in our muscles coupled with our kinetic energy inn backward direction, but when we try to stop a moving object we do negative work and yet again we produce thermal energy and KE in backward direction, so where is the distinction of positive and negative work in these cases...?? when KE is reduced shouldnt it be conserved as PE in some place?

Hello Satwik,

The polarity of work done on an object is determined by whether its kinetic energy increased or decreased. If you get in front of a object moving to the right, and exert a force to stop it, while you are stopping it you perhaps have to take a step backwards (to the right) while exerting the force to the left. (Or perhaps you only have to let your elbows flex.) The work formula is
W = F*d
where F and d are vectors pointing in opposite directions. Therefore W has a negative value. And the object's KE decreased to zero. You did negative work on the object.

Instead of using your body to stop it, you could put a spring in its path so that the object will compress a spring while it slows to a stop. In that case, the object's KE is converted to spring potential energy (assuming zero friction). The spring did negative work on the object. You could also say that the object did positive work on the spring. Similarly in the 1st case where you stopped it with your body, the object did positive work giving up its kinetic energy to accomplish that work. As Newton's 3rd Law says, as you exerted a force on the object, the object exerted a force on you. From the object's point of view, the vectors F and d in the work formula both point to the right.

My physics book is careful when discussing the work energy theorem to refer to the force involved as the resultant of forces on the object. If friction is involved and you're moving it at constant velocity, the resultant force on the object is zero. You are doing work but it is on friction -- the object's KE was not increased. If you quit pushing and the object slides to a stop due to the friction, negative work is done by the friction. PE is not involved assuming the floor is level. If you were pushing it up a slight incline and let it slide to a stop, then the part of the KE was converted to PE and the rest was dissipated while friction did negative work on it.

I hope this helps,
Steve
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Physics

Volunteer

#### Steve Johnson

##### Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

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I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

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BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University