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Work, Power, and Machines

What is Work?

- transfer of energy to a body by application of a

force that causes body to move in direction of

force. - W F ? d

What is Work?

Chapter 12

- SI units
- joules (J).
- 1 J 1 Nm 1 kgm2/s2

WORK

- Imagine a father playing with his daughter by

lifting her repeatedly in the air. How much work

does he do with each lift, assuming he lifts her

2.0 m and exerts an average force of 190 N?

GIVEN W ? F 190 N d 2.0 m

WORK W Fd W (190 N) (2.0 m) W 380 J

WORK

- A crane uses an average force of 5200 N to lift

a girder 25 m. How much work does the crane do

on the girder?

GIVEN W ? F 5200 N d 25 m

WORK W Fd W (5200 N) (25 m) W 130,000 J or

1. 3 x 105 J

WORK

- An apple weighing 1 N falls through a distance

of 1 m. How much work is done on the apple by

the force of gravity?

GIVEN W ? F 1 N d 1m

WORK W Fd W (1 N) (1 m) W 1 J

Power

Chapter 12

- rate at which work is done or energy is

transformed. - SI Unit
- watts.
- watt (W) 1 J/s
- Power work
- time

p W/t

POWER

- It takes 100 kJ of work to lift an elevator 18

m. If this is done in 20 s, what is the average

power of the elevator during the process?

GIVEN p ? W 1 x 105 J t 20 s

WORK p W/t p 1 x 105 J / 20 s p 5 x 103 W

or 5 kW

POWER

- While rowing across the lake during a race, John

does 3960 J of work on the oars in 60.0 s. What

is his power output in watts?

GIVEN p ? W 3960 J t 60 s

WORK p W/t p 3960 J / 60 s p 66.0 W

POWER

- Using a jack, a mechanic does 5350 J of work to

lift a car 0.500 m in 50.0 s. What is the

mechanics power output?

GIVEN p ? W 5350 J t 50 s

WORK p W/t p 5350 J / 50 s p 107 W

Machines

- Machines
- multiply and redirect forces.
- help people by redistributing work put into them.
- change either size or direction of input force.
- allows same amount of work to be done by
- either decreasing distance while increasing force

or - by decreasing force while increasing distance.

Force and Work

Chapter 12

Mechanical Advantage

- tells how much a machine multiplies force or

increases distance. - mechanical advantage output force input

distance - input force output distance

MECHANICAL ADVANTAGE

- Calculate the mechanical advantage of a ramp

that is 5.0 m long and 1.5 m high.

GIVEN ma ? id 5.0 m od 1.5 m

WORK ma id/od ma 5.0 m / 1.5 m ma 3.3

MECHANICAL ADVANTAGE

- Calculate the mechanical advantage of a ramp

that is 6.0 m long and 1.5 m high.

GIVEN ma ? id 6.0 m od 1.5 m

WORK ma id/od ma 6.0 m / 1.5 m ma 4

MECHANICAL ADVANTAGE

- Determine the mechanical advantage of an

automobile jack that lifts a 9900 N car with an

input force of 150 N.

GIVEN ma ? of 9900 N if 150 N

WORK ma of/if ma 9900 N / 150 N ma 66

SIMPLE MACHINES

The Lever Family

- simple machines
- One of six basic types of machines which are

basis for all other forms of machines. - have a rigid arm and a fulcrum.
- six types divided into two families.

First Class Levers

- fulcrum located between points of application of

input and output forces.

Second Class Levers

- fulcrum is at one end of arm and input force is

applied to other end.

Third Class Levers

- multiply distance rather than force.
- have a mechanical advantage of less than 1.

Pulleys

- are modified levers.
- point in middle of a pulley is like fulcrum of a

lever. - single, fixed pulley has a m. a. of 1.
- block and tackle Multiple pulleys working

together

Wheel Axle

- a lever or pulley connected to a shaft.
- steering wheel of a car, screwdrivers, and cranks

The Inclined Plane Family

- multiply and redirect force.
- turns small input force into large output force

by spreading work out over a large distance.

Simple Inclined Plane

- Changes both magnitude direction of force

Wedge

- Functions as two inclined planes back to back.
- Turns single downward force into two forces

directed out to sides.

Screw

- an inclined plane wrapped around a cylinder.

Compound Machines

Chapter 12

- machine made of more than one simple machine
- Examples
- scissors
- two first class levers joined at a common fulcrum
- car jack
- combination of lever with a large screw

What is Energy?

Energy

Chapter 12

- Energy
- ability to do work.
- When you do work on an object, you transfer

energy to that object. - Whenever work is done, energy is transformed or

transferred to another system. - SI Units joules (J)

Potential Energy

- energy that an object has because of position,

shape, or condition - stored energy.
- Elastic potential energy
- energy stored in any type of stretched or

compressed elastic material, (spring or a rubber

band). - Gravitational potential energy
- energy stored in gravitational field which exists

between any two or more objects.

Gravitational Potential Energy

- depends on both mass and height.
- PE mgh
- The height can be relative.
- height used in above equation is usually measured

from ground. - However, it can be a relative height between two

points, such as between two branches in a tree.

GRAVITATIONAL POTENTIAL ENERGY

- A 65 kg rock climber ascends a cliff. What is

the climbers gravitational potential energy at a

point 35 m above the base of the cliff?

GIVEN m 65 kg h 35 m g 9.8 m/s2 PE ?

WORK PE mgh PE (65 kg) (35 m) (9.8 m/s2) PE

2.2 x 104 kgm2/s2 2.2 x 104 J

Kinetic Energy

- energy of a moving object due to objects motion
- depends on mass and speed.
- depends on speed more than mass.

KINETIC ENERGY

- What is the kinetic energy of a 44 kg cheetah

running at 31 m/s?

GIVEN KE ? m 44 kg v 31 m/s

WORK KE ½ mv2 KE ½ (44 kg) (31 m/s)2 KE

2.1 x 104 kg x m2/s2 or 2.1 x104 J

KINETIC ENERGY

- Calculate the kinetic energy in joules of a 1500

kg car moving at 29 m/s.

GIVEN KE ? m 1500 kg v 29 m/s

WORK KE ½ mv2 KE ½ (1500 kg) (29 m/s)2 KE

6.3 x105 J

KINETIC ENERGY

- Calculate the kinetic energy in joules of a 1500

kg car moving at 18 m/s.

GIVEN KE ? m 1500 kg v 18 m/s

WORK KE ½ mv2 KE ½ (1500 kg) (18 m/s)2 KE

2.4 x105 J

Other Forms of Energy

- mechanical energy
- amount of work an object can do because of

objects kinetic potential energies - you can SEE it
- Large scale basis
- nonmechanical energy.
- you CANNOT SEE it
- X rays, microwaves
- Small scale basis (atomic)

Other Forms of Energy

Chapter 12

- Atoms and molecules
- kinetic energy of particles related to heat and

temperature. - Chemical reactions
- Breaking bonds exothermic/endothermic
- Photosynthesis
- turn energy in sunlight into chemical energy.

Other Forms of Energy

- nuclear fusion reactions
- Combining of atomic nuclei
- Electricity.
- derived from flow of charged particles
- bolt of lightning or in a wire.
- electromagnetic waves.
- Light energy from sun

CONSERVATION OF ENERGY

Energy Transformations

- readily changes from one form to another.
- Potential energy changes into kinetic energy.
- car goes down a hill on a roller coaster,

potential energy changes to kinetic energy. - Kinetic energy changes into potential energy.
- kinetic energy a car has at bottom of a hill can

do work to carry car up another hill.

Energy Transformations

- Mechanical energy can change to
- nonmechanical energy as a result of
- friction,
- air resistance,
- or other means.

The Law of Conservation of Energy

- energy cannot be created or destroyed.
- doesnt disappear, it changes to another form.
- if total energy in a system increases, it must be

due to energy that enters the system from an

external source.

SYSTEMS

- closed system
- when flow of energy into and out of a system is

small enough that it can be ignored - open systems (most)
- exchange energy with the space that surrounds

them.

Efficiency of Machines

- Not all of the work done by a machine is useful

work. - cannot do more work than work required to operate

machine. - Because of friction, work output of a machine is

always somewhat less than work input. - Efficiency
- ratio of useful work out to work in.
- measure of how much useful work it can do.
- expressed as a percentage.

Efficiency of Machines

- Efficiency Equation

- Machines need energy input.
- Because energy always leaks out of a system,

every machine needs at least a small amount of

energy input to keep going.

EFFICIENCY

- A sailor uses a rope and an old, squeaky pulley

to raise a sail that weighs 140 N. He finds that

he must do 180 J of work on the rope in order to

raise the sail by 1 m (doing 140 J of work on the

sail). What is the efficiency of the pulley?

Express your answer as a percentage.

GIVEN eff ? uwo 140 J wi 180 J

WORK eff uwo/wi eff 140 J / 180 J eff 0.78

or 78

EFFICIENCY

- Alice Jim calculate that they must do 1800 J

of work to push a piano up a ramp. However,

because they must also overcome friction, they

must actually do 2400 J of work. What is the

efficiency of the ramp?

GIVEN eff ? uwo 1800 J wi 2400 J

WORK eff uwo/wi eff 1800 J / 2400 J eff

0.75 or 75

EFFICIENCY

- It takes 1200 J of work to lift the car high

enough to change a tire. How much work must be

done by the person operating the jack if the jack

is 25 efficient

GIVEN eff 25 uwo 1200 J wi ?

WORK wi uwo/eff wi 1200 J / .25 wi 4800 J