Chapter 4 Machines, Chapter 4 Machines, Work, and EnergyWork, and Energy

4.2 Simple Machines4.2 Simple Machines

What is a Machine?What is a Machine? A machine is a device with moving parts A machine is a device with moving parts

that work together to accomplish a task.that work together to accomplish a task. A bicycle is made of a combination of A bicycle is made of a combination of

machines that work together. machines that work together. All the parts of a bicycle work as a system All the parts of a bicycle work as a system

to transform forces from your muscles to transform forces from your muscles into motion.into motion.

A bicycle allows you to travel A bicycle allows you to travel

at faster speeds and for at faster speeds and for

greater distances than greater distances than

possible on foot.possible on foot.

The Concepts of Input and The Concepts of Input and OutputOutput

Machines are designed to do something.Machines are designed to do something. The input includes everything you do to make The input includes everything you do to make

the machine work, like pushing on the bicycle the machine work, like pushing on the bicycle pedals.pedals.

The output is what the machine does for you, The output is what the machine does for you, like going fast or climbing a steep hill.like going fast or climbing a steep hill.

The input and output may be force, power, or The input and output may be force, power, or energy.energy.

The Beginning of TechnologyThe Beginning of Technology

A simple machine is an unpowered A simple machine is an unpowered mechanical device that accomplishes a mechanical device that accomplishes a task with only one movement (such as a task with only one movement (such as a lever).lever).

A lever allows you to move a rock that A lever allows you to move a rock that weighs 10 times (or more) what you weighs 10 times (or more) what you weigh.weigh.

Input Force and Output Input Force and Output ForceForce

Simple machines work with forces. Simple machines work with forces. The input force is the force you apply to the The input force is the force you apply to the

machine.machine. The output force is the force the machine The output force is the force the machine

applies to what you are trying to move.applies to what you are trying to move.

Ropes and PulleysRopes and Pulleys

A rope and pulley A rope and pulley system is a simple system is a simple machine made by machine made by connecting a rope to connecting a rope to one or more pulleys.one or more pulleys.

You apply the input You apply the input force to the rope and force to the rope and the output force is the output force is exerted on the load exerted on the load you are lifting.you are lifting.

Machines within MachinesMachines within Machines

Most of the Most of the machines we use machines we use today are made up today are made up of combinations of of combinations of different types of different types of simple machines.simple machines.

Types of MachinesTypes of Machines

Bicycle uses wheels Bicycle uses wheels and axels, levers (the and axels, levers (the pedals and kickstand), pedals and kickstand), and gears.and gears.

A complex machine like a A complex machine like a VCR contains simple VCR contains simple machines of every type machines of every type including screws, ramps, including screws, ramps, pulleys, wheels, gears, pulleys, wheels, gears, and levers.and levers.

Ratio of Output to Input Ratio of Output to Input ForceForce

The mechanical advantage of a machine is the ratio of The mechanical advantage of a machine is the ratio of the output force to the input force.the output force to the input force.

If the mechanical advantage of a machine is larger If the mechanical advantage of a machine is larger than one, the output force is larger than the input force.than one, the output force is larger than the input force.

A mechanical advantage smaller than one means the A mechanical advantage smaller than one means the output force is smaller than the input force.output force is smaller than the input force.

Mechanical advantage is a ratio of forces, so it is a Mechanical advantage is a ratio of forces, so it is a pure number without any units.pure number without any units.

Input and Output WorkInput and Output Work

A simple machine does work because it A simple machine does work because it exerts forces over a distance. exerts forces over a distance.

If you are using the machine you also do If you are using the machine you also do work, because you apply forces to the work, because you apply forces to the machine that move its parts.machine that move its parts.

Definition of a Simple Definition of a Simple MachineMachine

A simple machine has no source of energy A simple machine has no source of energy except the immediate forces you apply.except the immediate forces you apply.

The only way to get output work FROM a The only way to get output work FROM a simple machine is to do input work ON the simple machine is to do input work ON the machine.machine.

The output work done by a simple machine can The output work done by a simple machine can never exceed the input work done on the never exceed the input work done on the machine.machine.

Perfect MachinesPerfect Machines

In a In a perfectperfect machine, the output work machine, the output work equals the input work. equals the input work.

Friction always converts some of the input Friction always converts some of the input work to heat and wear, work to heat and wear,

so the output work is so the output work is

always always lessless than the than the

input work.input work.

The Cost of Multiplying ForceThe Cost of Multiplying Force

The output work of a machine can never The output work of a machine can never be greater than the input work.be greater than the input work.

This rule is true for all machines.This rule is true for all machines. The force and distance are related by the The force and distance are related by the

amount of work done.amount of work done. In a perfect (theoretical) machine, the In a perfect (theoretical) machine, the

output work is exactly equal to the input output work is exactly equal to the input work.work.

Force or DistanceForce or Distance

Many problems give Many problems give three or four quantities: three or four quantities: input force, input input force, input distance, output force, distance, output force, and output distance. and output distance.

If the input and output If the input and output work are equal then force work are equal then force x distance at the input of x distance at the input of the machine equals force the machine equals force x distance at the output.x distance at the output.

Parts of the LeverParts of the Lever

All levers include a stiff structure that rotates All levers include a stiff structure that rotates around a fixed point called thearound a fixed point called the fulcrum fulcrum..

The side of the lever where the input force is The side of the lever where the input force is applied is called the applied is called the input arminput arm. .

The The output armoutput arm is the end of the lever that applies is the end of the lever that applies the output force.the output force.

Load

Effort

Fulcrum

Changing DirectionChanging Direction

When the fulcrum is in the middle of the lever, When the fulcrum is in the middle of the lever, the input and output forces are the same.the input and output forces are the same.

The input and output forces are different if the The input and output forces are different if the fulcrum is not in the center of the lever.fulcrum is not in the center of the lever.

The side of the lever with the longer arm has The side of the lever with the longer arm has the smaller force.the smaller force.

Input work Output work di x Fi = do x Fo

di = Fo

do Fi

Mechanical Advantage of a Mechanical Advantage of a LeverLever

The output work is the output force The output work is the output force multiplied by the output distance.multiplied by the output distance.

The input work is the input distance The input work is the input distance multiplied by the input force. multiplied by the input force.

Mechanical Advantage of a Mechanical Advantage of a LeverLever

By setting the input By setting the input and output work and output work equal, you see that equal, you see that the ratio of forces is the ratio of forces is the inverse of the the inverse of the ratio of distances.ratio of distances.

The larger (input) The larger (input) distance has the distance has the smaller force. smaller force.

The ratio of distances The ratio of distances is equal to the ratio of is equal to the ratio of the lengths of the two the lengths of the two arms of the lever. arms of the lever.

Three Types of LeversThree Types of Levers

Levers are used in Levers are used in many common many common machines: pliers, machines: pliers, wheelbarrow, and wheelbarrow, and the human biceps the human biceps and forearm.and forearm.

The mechanical The mechanical advantage is advantage is always the ratio of always the ratio of lengths of the input lengths of the input arm to the output arm to the output arm.arm.

How a Rope and Pulley How a Rope and Pulley System WorksSystem Works

The force in a rope is called tension and is a pulling The force in a rope is called tension and is a pulling force that acts along the direction of the rope.force that acts along the direction of the rope.

The tension is the same at every point in a rope.The tension is the same at every point in a rope. If the rope is not moving, its tension is equal to the If the rope is not moving, its tension is equal to the

force pulling on each end.force pulling on each end. Ropes or strings do Ropes or strings do notnot carry pushing forces. carry pushing forces.

Mechanical AdvantageMechanical Advantage

The mechanical advantage of a The mechanical advantage of a pulley system depends on the pulley system depends on the number of strands of rope directly number of strands of rope directly supporting the load.supporting the load.

To make a rope and pulley system To make a rope and pulley system with a greater mechanical with a greater mechanical advantage, you can increase the advantage, you can increase the number of strands directly number of strands directly supporting the load by taking more supporting the load by taking more turns around the pulleys.turns around the pulleys.

Gears and RampsGears and Ramps

Many machines require that rotating motion Many machines require that rotating motion be transmitted from one place to another. be transmitted from one place to another.

The transmission of rotating motion is often The transmission of rotating motion is often done with gears. done with gears.

Some machines that use gears, such as small Some machines that use gears, such as small drills, require small forces at high speeds. drills, require small forces at high speeds.

Other machines, such as the paddle wheel on Other machines, such as the paddle wheel on the back of a steamboat, require large forces the back of a steamboat, require large forces at low speed.at low speed.

How Gears WorkHow Gears Work

The rule for how two gears turn depends The rule for how two gears turn depends on the number of teeth on each gear.on the number of teeth on each gear.

RampsRamps

A ramp is another type of simple machine that allows A ramp is another type of simple machine that allows you to push a heavy object to a higher location with you to push a heavy object to a higher location with less force than is needed to lift the object straight up.less force than is needed to lift the object straight up.

Ramps reduce the input force needed by increasing Ramps reduce the input force needed by increasing the distance over which the input force acts. the distance over which the input force acts.

The output work is work done against gravity.The output work is work done against gravity.

Mechanical Advantage of a RampMechanical Advantage of a Ramp

The input work is the input force The input work is the input force multiplied by the length of the ramp. multiplied by the length of the ramp.

Mechanical advantage = ramp length

height

10m1m

Ramp

ScrewsScrews

A screw is a simple A screw is a simple machine that turns machine that turns rotating motion into rotating motion into linear motion. linear motion.

A screw works just like A screw works just like a ramp that curves as it a ramp that curves as it get higher. get higher.

The “ramp” on a screw The “ramp” on a screw is called a thread.is called a thread.