WORK AND ENERGY

SIMPLE MACHINES

WORK

It takes energy to move something.

– The energy required to move it is called work.

Work is force applied over a distance.

W = F x d

He may expend energy when he pushes on the wall, but if it doesn’t move, no work is done on the wall.

WORK

W = F x d – Remember

Force units – Newtons (N) Distance units– Meters (m)

Work units then = Nm = a Joule (J) Ex. How much work is done on a 60N box that is

lifted 2.5m off the floor? Answer:

– W = F x d – W = 60N x 2.5m – W = 150J

Joule, James (1818-1889)

English physicist WORKED ON HEAT TRANSFER

Work

Work depends on two factors:

– Distance over which the force is applied

– Amount of force applied

When a load is lifted two stories high, twice the work

is done because the distance is twice as much.

When two loads are lifted to the same height, twice as much work is done because the force needed to lift them is twice as much.

Concept check

How much work is needed to lift an object that weighs 500 N to a height of 4 m?

W = F × d = 500 N × 4 m = 2000 J.

How much work is needed to lift it twice as high?

Twice the height requires twice the work. That is, W = F × d =

500 N × 8 m = 4000 J.

How much work is needed to lift a 1000 N to a height of 8 m?

Lifting twice the load twice as high requires four times the work.

That is, F × d = 1000 N × 8 m = 8000 J.

POWER

Lifting a load quickly is more difficult than lifting the same load slowly. If equal loads are lifted to the same height, the forces and distances are equal, so the work is the same. What’s different is the power.

Power – is the rate at which energy is changed from

one form to another.

– Also, power is the rate at which work is done.

POWER

POWER equals the amount of work done divided by the time interval during which the work occurs.

POWER = work / time

The unit of power is the joule per second, called the watt (W).

James Watt 1736-1819

Scottish Inventor STEAM ENGINE

Concept check

You do work when you do push-ups. If you do the same number of push-ups in half the time, how does your power output compare?

Your power output is twice as much.

How many watts of power are needed when a force of 1 N moves a book 2 m in a time of 1 s?

P = W/t = (F x d) / t = (1 x 2) / 1 = 2 Watts

Practice

Work on the problems on page 678 of the text book.

p 678 calculating power 1-3

Show all work.

MECHANICAL ENERGY

When raised, the ram then has the ability to do work on a piling beneath it when it falls.

When work is done by an archer in drawing a bow, the bent bow has the ability to do work on the arrow.

When work is done to wind a spring mechanism, the spring then has the ability to do work on various gears to run a clock, ring a bell, or sound an alarm.

MECHANICAL ENERGY

This ability to do work is energy.

– Like work, energy is measured in joules.

Energy appears in many forms, such as heat, light, sound, electricity, and radioactivity.

– It even takes the form of mass, as celebrated in Einstein’s famous E = mc2 equation.

Potential and kinetic energy are both considered to be kinds of mechanical energy.

POTENTIAL ENERGY

In the stored state, energy has the potential to do work. Therefore, it is called potential energy (PE).

The potential energy due to elevated position is called gravitational potential energy.

The amount of gravitational potential energy possessed by an elevated object is equal to the work done against gravity in lifting it. – Gravitational potential energy = weight × height

– PE = mgh

POTENTIAL ENERGY

The PE of the 10-N ball is the same (30 J) in all three cases.

Concept check

How much work is done in lifting the 200-N block of ice shown in Figure a vertical distance of 2.5 m?

500 J. (We get this either by Fd or mgh.)

How much work is done in pushing the same block of ice up the 5-m long ramp? The force needed is only 100 N (which is why inclines are used).

500 J. (She pushes with half the force over twice the distance.)

What is the increase in the block’s potential energy in each case?

Either way increases the block’s potential energy by 500 J. The ramp simply makes

this work easier to perform.

KINETIC ENERGY

A moving object is capable of doing work. – It has energy of motion

– kinetic energy (KE).

The kinetic energy of an object depends on its mass and speed.

More massive = more energy

Higher speed = more energy

Kinetic energy = 1/2 mass × speed2

KE = 1/2 mv2

Concept Check

A car travels at 30 km/h and has kinetic energy of 1 MJ. If it travels twice as fast, 60 km/h, how much kinetic energy will it have?

Twice as fast means (22) four times the kinetic energy, or 4 MJ.

If it travels three times as fast, at 90 km/h, what will be its kinetic energy?

Three times as fast means (32) nine times the kinetic energy, or 9 MJ.

If it travels four times as fast, at 120 km/h, what will be its kinetic energy?

Four times as fast means (42) sixteen times the kinetic energy, or 16 MJ.

WORK-ENERGY THEOREM

Work-energy theorem

– The change in kinetic energy is equal to the work done

– Work = DKE

Applies to potential energy as well

No change in energy means no work done

Changing the energy means there has to be work done.

WORK-ENERGY THEOREM

The theorem also applies to decreasing speed.

Decreasing KE requires work

This work is the friction supplied by the brakes, multiplied by the distance over which the force acts.

– Since friction is the same for a given set of brakes/tires/road, it is the distance that is affected when trying to stop at different speeds.

WORK-ENERGY THEOREM

Remember that a car traveling twice as fast would have 4 times the energy and would require 4 times the work to stop it.

This means 4 times the stopping distance.

Concept Check

When the brakes of a car are locked, the car skids to a stop. How much farther will the car skid if it’s moving 3 times as fast?

Nine times farther. The car has nine times as much

energy when it travels three times as fast: 1/2 m(3v)2 = 1/2 m9v2 = 9(1/2 mv2). The friction force will ordinarily be the same in either case. Therefore, to do nine times the work requires nine times as much sliding distance.

Conservation of Energy

The Law of Conservation of Energy

– Energy cannot be created or destroyed; it may be transformed from one form into another or transferred from one object to another, but the total amount of energy never changes.

Concept Check

The values of kinetic energy and potential energy for the block freely sliding down a ramp are shown only at the bottom of the ramp. Fill in the missing values.

Simple Machines

Simple Machines – Multiply forces

– Change the direction of forces

They may decrease the effort required but they do not reduce the amount of work. – Actually more work is needed due to the friction in

the machine.

Mechanical Advantage – How much the machine multiplies the effort force.

Resistance Force / Effort Force – actual MA

Effort distance / Resistance distance – Ideal MA

Simple Machines

Any machine that multiplies force does so at the expense of distance.

Likewise, any machine that multiplies distance does so at the expense of force.

No machine or device can put out more energy than is put into it.

No machine can create energy; it can only transfer it or transform it from one form to another.

Simple Machines

There are a few basic simple machines

– Levers

– Pulleys

– Inclined planes

– Wedges

– Wheel and axle

– Screws

– Hydraulic presses

Levers

Lever – A bar or rod that pivots on a fulcrum.

There are three classes of levers

Pulleys

Pulley a rope that turns around a wheel.

There a re three basic types of pulleys.

Combination-Note the load is supported by 7 strands of rope. Each strand supports 1/7 the load. The tension in the rope pulled by the man is likewise 1/7 the load.

Single movable-In this arrangement, a load can be lifted with half the input force.

Single fixed-This pulley acts like a lever. It changes only the direction of the input force.

Wheel and Axle

Wheel and Axle

– A wheel and axle has a larger wheel (or wheels) connected by a smaller cylinder (axle) and is fastened to the wheel so that they turn together.

– A lever in the round

– Doorknobs

– Wrenches

– Steering wheels

Inclined Planes

Inclined Plane- is a slope or a ramp.

– It can be any slanted surface used to raise a load from a lower level to a higher level.

Wedges

Wedge- a moving inclined plane

– Wedges move into the resistance

– Usually used for cutting purposes

– They change the direction of the force applied.

Screws

Screw- an inclined plane wrapped around a cylinder.

– Space saving

Hydraulic Press A combination of a large and

a small cylinder connected by a pipe and filled with a fluid so that the pressure created in the fluid by a small force acting on the piston in the small cylinder will result in a large force on the large piston. The operation depends upon Pascal's principle, which states that when a liquid is at rest the addition of a pressure (force per unit area) at one point results in an identical increase in pressure at all points.

Efficiency

Efficiency is defined as the ratio of work output to work input

Efficiency = work output work input

Nothing is 100% efficient – Friction, friction, friction

– Energy converts to heat (molecular level Kinetic Energy)

Sources of Energy Nuclear Energy

– Most forms can be traced back to the sun

Coal, solar, petroleum, natural gas, wood, wind, flowing water.

– Nuclear reactions in Earth’s interior

Volcanic, geothermal