9.1 Work

“How long” need not always mean time. It can also mean distance. When considering the quantity force x distance, we are talking about the concept of work.

Work is the product/result of the net force on an object and the distance through which the object is moved. We do work when we lift a load against Earths gravity. The heavier the load or higher we lift, the more work we do.

Work is done when a force acts on an object and the object moves in the direction of the force.

Work = net force x distance

W = fd

If we lift two loads up one story, we do twice as much work as we would lifting one load up one story in the same distance, because the force needed to lift twice the weight is twice as great. Similarly, if we lift one load two stories instead of one story, we do twice as much work because the distance is twice as great.

Work is generally falls into two categories:

1. work is done against another force

   1. when an archer stretches her bowstring, she is doing work against the elasticity.

   2. when the ram of a pile driver is raised, work is required to raise the ram against the force of gravity.

   3. when you do a push-up, you work against your own weight.

You do work on something when you force it to move against the influence of an opposing force—often friction.

2. work is done to change the speed of an object

   1. bringing an automobile to speed up or slow down

In both categories, work involves a transfer of energy between something and its surroundings

9.2 Power

The definition of work says nothing about how long it takes to do the work. When carrying a load up some stairs, you do the same amount of work whether you walk or run up the stairs. So why are you more tired after running upstairs in a few seconds than after walking upstairs in a few minutes?

Power is the rate at which work is done.

Power equals the amount of work done divided by the time interval during which the work is done.

Power = work done/time interval

The unit of power is the joule per second, also known as watt.

9.3 Mechanical Energy

When work is done by an archer in drawing back a bowstring, the bent bow acquires the ability to do work on the arrow. When work is done to stretch a rubber band, the rubber band acquires the ability to do work on an object it is released.

The property of an object or system that enables it to do work is energy. Like work, energy is measured in joules.

Mechanical energy is the energy due to positions of something or the movement of something.

The two forms of mechanical energy are kinetic energy and potential energy.

9.4 Potential Energy

Energy that is stored and held in readiness is called potential energy because in the stored state it has the potential for doing work.

Three examples of potential energy are elastic potential energy, chemical energy, and gravitational energy.

Elastic Potential Energy

A stretched or compressed spring, for example, has potential for doing work.

• Ex. when a bow is drawn back, energy is stored in the bow. the bow can do work on the arrow.

A stretched rubber band has potential energy because of its position.

Chemical Energy

Chemical energy in fuels is also potential energy. It is actually energy of position at the subatomic level. Potential energy is found in fossil fuels, electric, and food and we eat.

Gravitational Potential Energy

Work is required to elevate objects against Earth’s gravity. The potential energy due to elevated position is gravitational potential energy.

The amount of gravitational potential energy possessed by an elevated object is equal to the work against gravity in lifting it.

PE = mgh

9.5 Kinetic Energy

Push on an object and you can set it in motion. If an object is moving, then it is capable of doing work. It has energy in motion, or kinetic energy. The kinetic energy of an object depends on the mass of the object as well as its speed.

Kinetic energy = ½ mass x speed²

9.6 Work-energy Theorem

The work-energy theorem describes the relationship between work and energy.

The work-energy theorem states that whenever work is done, energy changes.

Work = ∆KE

The more kinetic energy something has, the more work is required to stop it. Twice as much kinetic energy means twice as much work.

9.7 Conservation of Energy

As you draw back the arrow in a bow, you do work stretching the bow. The bow then has potential energy. When released, the arrow has kinetic energy equal to this potential energy.

The study of the various forms of energy and the transformations from one form into another is the law of conservation of energy.

The law of conservation of energy states that energy cannot be created nor destroyed. It can be transformed from one form into another, but the total amount of energy never changes.

9.8 Machines

A machine is a device used to multiply forces or simply to change the direction forces. The concept that underlies every machine is the conservation of energy. A machine cannot put out more energy than is put into it.

A machine transfers energy from one place to another or transforms it from one form to another.

Levers

A lever is a simple machine made of a bar that turns on a fixed point. At the same time we do work on one end of the lever, the other end does work on the load.

work input = work output