# Work, Energy, and Simple Machines

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Work, Energy, and Simple Machines

Work Work equals force times distance where distance is in the direction of the force applied.(scalar) Work is measured in joules. 1 Joule = 1 Nm = 1 kgm2/s2. Since work is only done in the direction of force applied, pushing at an angle must require trig functions.

Work If you graph force versus displacement, you should get a straight line. The area under such a graph would be equal to the work.

Work W = Fcos q d Fy F Fx = Fcos q Fy = Fsin q Fx
The lawn exerts a force, friction, on the lawnmower. If the lawnmower moves at a constant speed, the horizontal component of the applied force is balanced by the force of friction. The angle between the force of friction and the direction of motion is Thus W= -Fd for the work done by the grass. Negative work means that work is being done on the grass by the mower. The positive sign of work done by you exerting force on the handle means you are doing work. W = Fcos q d Fy F Fx = Fcos q Fy = Fsin q Fx

What is the effect of doing work?
It is to give an object the ability to cause a change in itself or its surroundings. It gives an object energy. Work then results in a transfer of energy by mechanical means.

Power Power is the rate of doing work. It is the rate of energy transfer. It is the work per unit of time. It is measured in watts or Joules/s. P = W/t = Fd/t = Fvavg Horsepower is the old unit of power. 1hp = 746 watts Machines with different power ratings do the same work in different times.

Work-Energy Theorem Net work = change in kinetic energy
Net work = ½ mv2f - ½mv2i This allows us to think of kinetic energy as the work an object can do as it comes to rest, or the amount of energy stored in the object. For example, a moving hammer on the verge of striking a nail has KE and can therefore do work on a nail. Part of this energy drives the nail while part goes to warming the nail and hammer on impact.

Machines A machine eases the load by changing the magnitude or the direction of the force, but does not change the amount of work done. You put work into a machine----work input(wi). Work is done by the machine----work output(wo). Work output is always less than work input due to losses from frictional heating.

The force you exert on a machine is the effort force(Fe).
The force exerted by the machine is the resistance force(Fr). The ratio of the resistance force to the effort force is called the actual mechanical advantage(MA). If a machine has an MA of >1 then it increases the force applied. The ratio of the effort distance(de) to the resistance distance(dr) is called the ideal mechanical advantage(IMA).

Efficiency is defined as the ratio of output work to input work
Efficiency is defined as the ratio of output work to input work. It is usually found as a percent. In an ideal machine work output equals work input. Efficiency may also be defined as the ratio of MA to IMA.

Simple Machines There are six simple machines. All of them really fall into 2 groups.

Levers There are three kinds of levers---first class, second class, and third class. All levers have a fulcrum but it is not always in the middle of the lever. 1st class--- 2nd class--- 3rd class--- Fe Fr fulcrum fulcrum Fr Fe fulcrum Fe Fr

Levers in Action

Compound Machines When two or more simple machines are linked together so that the resistance force of one machine becomes the effort force of the second then they are known as a compound machine. The mechanical advantage of a compound machine is the product of the mechanical advantages of the simple machines from which it is made.