PHYSICS DOUBT -

Question

Can power be negative?

Like, if we are lifting a box weighing 10 kg above the ground to a height of 1m in 1 second, then the energy would be- mxgxh, that is 10kg x -9.8m/s^2 (because we are lifting it against the gravity) x 1m = -98J / 1sec = -98W

So is it possible?

Answer 1

In order to properly calculate work and power, it's important to keep careful track of what forces are being applied by which objects. In this case, the force m * g would actually be the force of gravity from the earth pulling downward on the box. The force being applied by the lifter would need to counteract that gravitational force; thus it has equal magnitude but opposite orientation. This of course coincides with the intuitive understanding that we are in fact lifting the object upwards. Since the force applied by the lifter is pointed in the same direction as the movement it effects, the sign of the power output is positive. One intuition check we could apply to confirm this comes from the fact that the object now has greater gravitational potential energy than before, due to its greater elevation.

However, it absolutely is possible in general for power output to be negative. For instance, if, instead of lifting the object upward, we we catch a falling object, our force is still directed upward, but since the overall movement of the object is downward, we calculate the work done by this force (and thus the corresponding power output) to be negative. A great example of this concept is the regenerative braking system incorporated into modern hybrid cars - in order to decelerate the car, the wheels are connected to electrical generators that convert the kinetic energy of the car's motion into electrical energy in the batteries. The force applied by the generators opposes the motion of the wheels, and thus negative work is done on them - another way of framing this is that the wheels are actually doing positive work on the generators!

The moral of the story here is that the sign of quantities like work and power gives you information about which direction energy is being transferred. When in doubt, try to leverage your understanding of the energy state of each element of the system before and after the interaction to figure out what sign makes the most sense.