10.2: Machines

And Mechanical Advantage

Machines make work easier Machines can change the direction of

force applied.

Machines can change the magnitude of force applied.

The work you do ON a machine is called work input, wi

The work done BY the machine is called work output, wo

Doing work transfers energy.

Conservation of Energy

Doing work with machines transfers energy from one source to another.

Work output can NEVER be greater than work input.

How helpful are machines?

Effort force, Fe, is the force you exert ON a machine.

Resistance force, Fr, is the force exerted BY a machine.

Mechanical Advantage is a ratio comparing resistance force to effort force. It has no units.

e

r

F

FMA

MA by the numbers

When a machine has a mechanical advantage >1, the machine increases the force you apply. (Fe < Fr)

If a machine has a mechanical advantage of 1, it changes the direction of your force. (Effort force = Resistance force)

A machine can increase force or distance, but it can NOT increase energy!

Breaking down work

Recall work = force x distance.

Work input = Fe x de (dist your hand moves)

Work output = Fr x dr (weight of the object x distance the object moves)

An IDEAL machine transfers ALL energy so

Wo = Wi or Frdr = Fede

By rewriting this equation as Fr/Fe = de/dr, ideal MA = de/dr

We measure distances moved for IMA, but forces exerted for Actual MA.

Efficiency

In real machines, not all work input comes out as useful work output. Some energy is converted into thermal energy or “lost” as heat.

This decreases the output of the machine.

Efficiency is a ratio of work output to work input OR Actual MA to Ideal MA.

100(%) xW

WEfficiency

i

o 100(%) xIMA

MAEfficiency

Simple Machines

The 6 simple machines include: lever, pulley, inclined plane, wedge, wheel and axle, and screw.

The IMA of all machines is the ratio of distances moved.

For levers and wheel and axles, the IMA is the ratio of effort distances (radius)/ resistance distances (radius) or re/rr as both machines have a “fixed” point or fulcrum.

Compound Machines

A compound machine is a combination of two or more simple machines linked together.

The resistance force of one machine becomes the effort force of the second.

In a bicycle, the pedal and front sprocket (gear) are like a wheel and axle. Fe is the force you exert on the pedal and Fr is the force the front sprocket exerts on the chain. The chain then exerts an Fe on the rear wheel sprocket. The Fr is the wheel on the road.

Compound Mechanical Advantages

The mechanical advantage of a compound machine is the product of the MAs of the simple machines making it up.

MA = MAmachine1 x MAmachine2

For the bicycle:

onpedal

onroad

bychain

onroad

onpedal

onchain

F

F

F

Fx

F

FMA

Example Problem

Look at the bicycle wheel example problem on page 237.

IMA = re/rr Fr = MA (Fe)

de = IMA(dr)

Fr

re

rr

Fe

Machines Applied

When a cyclist is on a hill, they can change the mechanical advantage needed to manipulate the terrain, by choosing the size of one or both sprockets.

Increasing the IMA increases the force the wheel exerts on the road. This is good for climbing a hill or accelerating.

On a level surface, less force is needed so the rider decreases the IMA by reducing the distance the pedals move each revolution.

The “simple” body machine? Principles of force and work can describe all motion

including our body.

Lever systems in the body allow us to walk and run.

Each lever has 4 parts:

1. A rigid bar (bone)

2. A source of force (muscle contractions)

3. A fulcrum or pivot point (joints b/t bones)

4. A resistance (weight of the body being moved)

These levers are not very efficient so exercise requires energy.

Your turn to Practice

Do Ch 10 Rev p 242 #s 13, 14, 16

Do p 244 #s 48, 51, & 53