# If I walk forward and stop was there work done?

If I'm on a flat surface and I start walking and go to a constant velocity, then I slow myself back down to a stop, was there work done?

I would think the answer is no because $work = force * distance$ and when I walk up to constant velocity I've applied a force times distance or work equal to what it takes to stop myself but in the opposite direction, so wouldn't the work cancel?

• Why will the work cancel? You had to get going, you had to slow down. – Jon Custer Jan 15 '16 at 20:42

The question is a bit vague, but the answer is yes.

In Thermodynamics and Physics in general, due to the conservation of energy, work is always a transfer of energy between different systems. So we have to talk of what systems we are thinking of.

Also, let's start with a simpler situation: consider just flexing your arm through your elbow, just like lifting an imaginary dumbbell. We consider three systems: your upper arm (bones and muscles) your bicep and your tricep.

Phase 1: Flexing (accellerating)

Your biceps contracts and starts pulling your arm upwards. It is applying a force on it for a certain distance: it is doing work. Your upper arm receives of energy, which is manifested in kinetic energy, while your muscles is losing energy: it is converting its internal chemical energy into the kinetic energy of your arm.

Phase 2: Stopping

Now to stop your fist from hitting your face, your triceps contracts, applying a force on your bones to stop them. Notice this time the force is resisting the movement: thus now the arm is losing energy (indeed, it stops) because it is doing work. The energy is transmitted into your tricep muscles, where it becomes heat.

Conclusion

In accelerating, your muscles do work on your body to get it moving; in stopping, they receive the same amount of work back. So work is being done. On the whole, (ignoring air friction and changes in gravitational energy), no work has been extracted from your body: you are just standing still again, slightly warmer.

• So the energy transfer between the earth and you would net 0 if you walked forward and stop I would think. Thanks for the detailed response, And thanks to everyone else for their input! – Rhezner Jan 15 '16 at 22:26
• Yes, web you start walking, the Earth adjusts rotating by conservation of momentum. When you stop, it returns to its original rotation. Net change in energy is 0. – Andrea Jan 17 '16 at 13:07

Work is a scalar quantity, which means it doesn't have a direction, unlike velocity or force. So you did work in speeding up and more in slowing down.. I.e the works adds together and doesn't cancel itself out.

• So there's no such thing as net work? It's always positive? Can't you have negative force and call it negative work? For whatever reason my physics teacher says negative work is a thing but that doesn't seem to make spence considering work is scalar. – Rhezner Jan 15 '16 at 20:40
• There is negative work. The work done by a spring when it is extended or compressed is negative. – Pranav Rastogi Jan 15 '16 at 20:57
• @Rhezner Of course there is negative work! The answers here are missing the mark. Scalars do indeed cancel! – Andrea Jan 15 '16 at 21:04