Workshop Tutorials for Introductory Physics
Solutions to MI6: Work, Power and Energy
A. Review of Basic Ideas:
Work energy and power
We use the words work, energy and power a lot in everyday life. You might tell someone to be quiet because you're trying to work on an assignment. Sports drinks give you energy to keep going for longer, and people brag about how powerful their cars are. We also use these words in physics, but with more precise meanings.
Work is the transfer of energy, to or from an object via a force. When energy is transferred to an object then the work done on the object is positive, if energy is transferred from an object then the work done on the object is negative. (This means that the object has done positive work on something else.)
If a force changes the speed at which an object is moving then the object's kinetic energy changes. The kinetic energy of an object with mass m moving at speed v is defined as KE = mv2. If the kinetic energy is the only type of energy changed by the action of a force then the work done is equal to the change in kinetic energy.
From Newton's laws we know that force is mass times acceleration, F = ma, and from kinematics we know that v2 = v02 +2as. Using this we discover that
W = KE = m (v2 - v02) = m (2as) = mas = Fs
To be strictly correct, because force is a vector quantity (it has direction) we should say that
= KE = Fs cos(.= .
where ( is the angle between the direction of the force F and the displacement x.
Lifting things can be very hard work. In this case if the object is lifted from rest to a higher position and put down so it is again at rest, such as carrying a suitcase upstairs, then the work done is the change in the object's gravitational potential energy. If you lift a heavy suitcase, carry it around an airport for a while, then put it down again, you haven't actually done any work, although you may feel like you have.
Power is the rate at which work is done, or energy is transferred. The power rating on the back of an appliance tells you how quickly it turns electrical energy into some other form of energy, such as light or heat.

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