Work, Energy, and Power
Energy takes many different forms – chemical, nuclear, kinetic, potential, heat, etc. In this chapter we concentrate on the two forms that comprise mechanical energy – kinetic and potential.
We begin with the related concept of work, defined as the product of force and distance (). Since force is measured in newtons and distance in meters, the proper unit for work is the newton-meter, which is called the joule. If the force is not directed along the displacement vector, then we take the part (component) of the force in the direction of the displacement in computing the work done. Work is a scalar quantity.
Power measures how fast work is done. It is defined as work divided by time
(P = W/t). The units are joules/second, called the watt.
The ability to do work is energy. It is measured in the same units (joules) as energy. Lifting an object against gravity requires work (a force equal to the weight of the object multiplied by the vertical height). In doing this work we have given the object energy (potential) which can be released again to do work.
Two forms of mechanical energy are recognized – kinetic and potential. Kinetic energy is energy of motion and is defined as one-half the mass times the velocity squared, or ½mv2. A very important theorm should also be common sense. The work-energy theorem tells us that the work down on an object is equal to the change in the kinetic energy. Consider a car accelerating from rest. Clearly we are doing work (a force is moving the car through distance) and the result of that work is that the car accelerates. The kinetic energy changes from zero (rest) to the final value. In symbols the work-energy theorem is W = DKE.
Potential energy is stored energy. In this chapter we consider only gravitational potential energy, the energy stored in a body by doing work against gravity. Gravitational potential energy is calculated as (mass)(acceleration of gravity)(vertical height) or mgh. Notice it is only the vertical height that matters. You can justify this since gravity only acts vertically. It does not matter how the object came to that height, only the height obtained. We say the potential energy is independent of path. Likewise the potential energy has an arbitrary zero point. We are free to choose the level of zero potential wherever we like.
Total mechanical energy is the sum of kinetic and potential energy. In the absence of dissipative forces (forces that cause energy to be lost to heat, such as friction or air resistance), total mechanical energy is conserved (doesn’t change). Conservation of Mechanical Energy can be applied when conservative forces are at work, such as gravity or spring forces.
This chapter also looked at simple machines. A machine in this sense is any device that amplified the force delivered. The work done on the input end is the same as the work delivered to the output end, but since work is force times distance, machines provide a situation for…
(FD)input = (Fd)output
Three type of simple machines are levers, inclined planes, and pulleys.