In the movie Happy Feet, when Mumble and his friends are trying to cross this barren area with blizzards, no matter how hard they resist, how much force they exert in the forward direction, they get blown away in the opposite direction. That's an example of negative work, right?
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Work is an interesting concept. It depends on which systems we are looking at.
The wind does positive work on the penguin (I'm assuming Mumble is a penguin as I haven't seen Happy Feet).
The penguin does positive work relative to the ice. (Assuming they move forward between gusts of wind.)
Now considering the penguin as the system. The net work on the penguin is negative.
The work of the penguin's legs is positive and the wind is negative (if the wind opposes the force of the legs). Since the penguin moves backwards, the net work ON THE penguin is negative.
WOah. THat's just wacky. :O
And by considering the penguin as a system, do you mean looking at it/considering it to be a whole?
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Yes. That comes from the definition of a system.
The penguin system does work on its surroundings with the objective of moving forward. This will be taken as the positive definition of work. The wind does work on the system by moving the system relative to its surroundings. Since the wind moves the penguin backwards (which we established as being the positive direction of work) the wind does negative work on the penguin system.
Since the net displacement of the penguin is backwards, the NET work on the SYSTEM is negative.
*light bulb on*.
Here's another situation - a guy's driving a car and applies the brakes. With respect to the frictional force of the road, the work done is positive. With respect to the motion of the car, the work done is negative. But, looking at the car as a system, the net work done is negative. Is that correct?
Be careful here. Is the friction force with the road the force that is causing the car to slow? Friction between the tires and the road is an interesting force in this case (assuming the wheels roll without slipping) because it actually doesn't do any work because the point of contact of the wheel has zero velocity, therefore the force of friction between the road and tires is that of the static type. In this case, the braking force is what applies the stopping force. The friction between the brake pads and the rotors is what creates this force. Since the rotors are moving relative to the brake pads, this is kinetic friction and does work.
If we look at the car system, brakes included, no work is done! Why? Several reasons. First, the braking force is an internal force. Work is done by external forces. Second, the brakes simply convert kinetic energy to thermal energy. Therefore, the net energy of the system doesn't change. (There are a couple of assumptions we make here.)
If we take the brakes as being separate from the system. They do negative work on the system as they decrease the kinetic energy of the system.