MachinesCh. 5 Sect. 2

Machines• A machine is a device that makes doing work easier

• Three ways that machines make work easier:

1. Increase the force that can be applied to an object• i.e. Screwdriver turning a screw, using a crowbar to pry something

open

2. Increase the distance over which a force can be applied • If work stays the same and distance increases, the required force

will be decreased• i.e. Pushing an object up a ramp

3. Change the direction of the applied force.• i.e. Using a car jack, chopping wood with an axe, opening/closing

blinds

Simple MachinesA machine that does work with only one movement of the machine

Types• Lever• Pulley• Wedge• Inclined Plane• Screw• Wheel & Axle

With a simple machine you can never increase both the force and the distance! If you gain one, you sacrifice (lose) the other.

Machines• There are two forces involved when a machine is used for

work:

1. Input force (Finput)– the force that is applied to the machine

2. Output force (Foutput)– the force that is applied by the machine

Machines• There are two kinds of work that need to be considered

1. Input work (Winput)- The work done by you on the machine

2. Output work (Woutput)- The work done by the machine

• Remember that energy is conserved. • When you do work you transfer energy to the machine. • When the machine does work on an object, energy is transferred to the

object. • Because energy cannot be created or destroyed, the amount of energy

transferred to the object cannot be greater than the amount of energy you transferred to the machine.

• Woutput is never greater than Winput.

Ideal vs. Real MachinesIdeal Machine• A perfect machine in which there was no friction.• No work would be “lost” to heat.

• For an ideal machine, Winput = Woutput.

Real Machine• For real machines, some of the energy put into a

machine is always converted into heat by frictional forces.

• Therefore, Woutput < Winput.

Efficiency• Efficiency is a measure of how much of the work

put into a machine is changed into useful output work by the machine.

• A high efficiency machine produces less heat from friction so more of the input work is changed to useful output work.

• Efficiency can be calculated by:

Efficiency• In an ideal machine there is no friction and the

output work equals the input work. So the efficiency of an ideal machine is 100%.

• In a real machine, friction causes the output work to always be less than the input work. So the efficiency of a real machine is always less than 100%.

Efficiency• Machines can be made more efficient by reducing

friction.

• This is usually done by adding a lubricant, such as oil or grease, to surfaces that rub together.

• A lubricant fills in the gaps between the surfaces, enabling the surfaces to slide past each other more easily.

Calculating Efficiency

• An inclined plane allows you to do 280 J of useful work on a refrigerator that you are sliding upward along the plane. If the work that you have to do is 760 J, what is the efficiency of the inclined plane?

• A lever requires you to push with 75N of force to move it 1 meter. The 125 N rock on the other end moved 0.3 m. What is the efficiency of this lever?

Win = 760 JWout = 280 J

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦=𝑤𝑜𝑟𝑘𝑜𝑢𝑡𝑝𝑢𝑡𝑤𝑜𝑟𝑘𝑖𝑛𝑝𝑢𝑡

𝑥100

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦=280 𝐽760 𝐽

𝑥100=37%

Win = 75 N x 1 m = 75 JWout = 125 N x 0.3 m = 37.5 J

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦=𝑤𝑜𝑟𝑘𝑜𝑢𝑡𝑝𝑢𝑡𝑤𝑜𝑟𝑘𝑖𝑛𝑝𝑢𝑡

𝑥100

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦=37.5 𝐽75 𝐽

𝑥100=50%