Work, Power, and Machines

Physical Science – Unit 7

Chapter 9

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Work

• What is work?– Work is the quantity of energy transferred

by a force when it is applied to a body and causes that body to move in the direction of the force.

• Examples:– Weightlifter raises a barbell over his/her

head

– Using a hammer

– Running up a ramp

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Work

Work in simple terms:

• Transfer of energy that occurs when a force makes an object move

• The object must move for work to be done

• The motion of the object must be in the same direction as the applied force

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Work

• The formula for work:– Work = force x distance

– W = F x d

• Measured in Joules (J)– Because work is calculated as force times

distance, it is measured in units of newtons times meters (N●m)

– 1 N●m = 1 J = 1 kg●m2/s2

• They are all equal and interchangeable!

James Joule - English scientist and inventor 1818-1889

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Work

• 1 J of work is done when 1N of force is applied over a distance of 1 m.

• kJ = kilojoules = thousands of joules

• MJ = Megajoules = millions of joules

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Practice problem

A father lifts his daughter 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?

W = F x d

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Practice problem

A father lifts his daughter 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?

W = F x d

W = 190 N x 2.0 m

= 380 N●m = 380 J

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Practice problems

A mover is moving about 200 boxes a day. How much work is he doing with each box, assuming he lifts each 10 m with a force of 250 N.

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Practice problems

A mover is moves about 200 boxes a day. How much work is he doing with each box, assuming he lifts each 10 m with a force of 250 N.

W = F x d

= 250 N x 10 m

= 2,500 N●m = 2,500 J

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Practice problems

A box with a mass of 3.2 kg is pushed 0.667 m across a floor with an acceleration of 3.2 m/s2. How much work is done on the box?

What do you need to calculate first?????

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Practice problems

A box with a mass of 3.2 kg is pushed 0.667 m across a floor with an acceleration of 3.2 m/s2. How much work is done on the box?

F = ma

= 3.2 kg x 3.2 m/s2

= 10.2 kg● m/s2 = 10.2 N

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Practice problems

A box with a mass of 3.2 kg is pushed 0.667 m across a floor with an acceleration of 3.2 m/s2. How much work is done on the box?

F = ma

= 3.2 kg x 3.2 m/s2

= 10.2 kg● m/s2 = 10.2 N

W = F x d

= 10.2 N x 0.667 m

= 6.80 N●m = 6.80 J

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• Practice problems

Get a calculator

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• Page 54 asks for distance……

W= F x D

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• #1

.6 m

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• #2

.6m

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• #3

2.6m

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• #4

2.398m

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• P55 asks for force

W= F x D

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• #5

2 800 000N

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• #6

27N

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• #7

900 000N

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• #8

95 454N

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• P56 asks for W………thank goodness

W= F x D

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• #9

237 825J

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• #10

3.2 x 106 J

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• #11

5 625 000 J

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• #12

2 127 840J

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How about a harder one….

#18

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• #18

• Calculate force first, then work

276 115J

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Power

• Power is a quantity that measures the rate at which work is done– It is the relationship between work and

time

– If two objects do the same amount of work, but one does it in less time. The faster one has more power.

• Rate at which work is done or how much work is done in a certain amount of time

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Power

• Formula for power:

Power = work

time

P = W/t

• SI units for power – watts (W)

• 1 kW – Kilowatt = 1000 watts

• 1 MW – Megawatt= 1 million watts

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Power

• A watt is the amount of power required to do 1 J of work in 1 s. (Reference – the power you need to lift an apple over your head in 1 s)

• Named for James Watt who developed the steam engine in the 18th century.

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Practice problems

A weight lifter does 686 J of work on a weight that he lifts in 3.1 seconds. What is the power with which he lifts the weight?

P = W/t

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Practice problems

A weight lifter does 686 J of work on a weight that he lifts in 3.1 seconds. What is the power with which he lifts the weight?

P = W = 686 J

t 3.1 s

221 J/s = 221 W

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Practice problems

• How much energy is wasted by a 60 W bulb if the bulb is left on over an 8 hours night?

P = W

t

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Practice problems

• How much energy is wasted by a 60 W bulb if the bulb is left on over an 8 hours night?

P = W

t

1st convert 8 hr to seconds

8 hr (60 min/1hr)(60 sec/1min) = 28800 sec

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Practice problems

• How much energy is wasted by a 60 W bulb if the bulb is left on over an 8 hours night?

P = W

t

1st convert 8 hr to seconds

8 hr (60 min/1hr)(60 sec/1min) = 28800 sec

2nd calculate for energy

W = P x t

= 60 W x 28800 sec

= 1.7 x 107 J

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• Practice problems

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• P58 asks for work

P= W/t

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• #1

412.5J

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• #2

1 710 000J

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• #3

7 500 000 J

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• #4

1.17 x 1010J

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• P59 asks for time

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• #5

955.36 sec

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• #6

456.14sec

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• #7

1 500sec

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• #8

4.5sec

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• P60 asks for power

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• #9

5 x 108 watts

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• #10

2.75 x 1010

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• Do 11 & 12

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• #11

300sec

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• #12

6 162 000J

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Machines and Mechanical Advantage

• Which is easier… lifting a car yourself or using a jack?

• Which requires more work?

• Using a jack may be easier but does not require less work. – It does allow you to apply less force at any

given moment.

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What is a machine?

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

• Machines increase the applied force and/or change the distance/direction of the applied force to make the work easier

• They can only use what you provide!

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Why use machines?

• If machines cannot make work, why use them?

– Same amount of work can be done by applying a small force over a long distance as opposed to a large force over a small distance.

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Effort and Resistance

• Machines help move things that resist being moved

• Force applied to the machine is effort force (aka: Input force)

• Force applied by the machine is resistance force (aka: Load, output force)

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Mechanical Advantage

• Mechanical advantage is a quantity that measures how much a machine multiplies force or distance

• Defined as the ratio between output force and input force

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Mechanical Advantage

• Mechanical advantage = output force

input force

• Mechanical advantage= input distance

output distance

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MachinesMachines MachinesMachines

Simple Machines

Lever Pulley Wheel & Axle

Inclined Plane Screw Wedge

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The Lever family

• Lever– a rigid bar that is free to pivot about a

fixed point, or fulcrum– Force is transferred from one part of the

arm to another.

“Give me a place to stand and I will move the Earth.”

– Archimedes

Engraving from Mechanics Magazine, London, 1824

Effort arm

Resistancearm

Fulcrum

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Lever

• First Class Lever– Most common type– Fulcrum in middle– can increase force, distance, or neither– changes direction of force

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Lever

• Second Class Lever– always increases force

– Resistance/load in middle

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Lever

• Third Class Levers– always increases distance

– Effort in middle

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Pulley

• Pulley– grooved wheel with a rope or chain

running along the groove

– a “flexible first-class lever” or modified lever

LeLr

F

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Pulley

• Ideal Mechanical Advantage (IMA)– equal to the number of supporting ropes

IMA = 0 IMA = 1 IMA = 2

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Pulley

• Fixed Pulley

IMA = 1

does not increase force

changes direction of force

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Pulley

• Movable Pulley

IMA = 2 increases forcedoesn’t change direction

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Pulley

• Block & Tackle

combination of fixed & movable pulleys increases force (IMA = 4) may or may not change direction

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Wheel and Axle

• Wheel and Axle

– two wheels of different sizes that rotate together

– a pair of “rotatinglevers”

– When the wheel is turned so so is the axle

Wheel

Axle

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Wheel and Axle

• Wheel and Axle

– Bigger the difference in size between the two wheels= greater MA

Wheel

Axle

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What is an inclined plane?

• A sloping surface, such as a ramp.

• An inclined plane can be used to alter the effort and distance involved in doing work, such as lifting loads.

• The trade-off is that an object must be moved a longer distance than if it was lifted straight up, but less force is needed.

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What is an inclined plane?

• MA=Length/Height

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Incline Plane Family

• A wedge is a modified incline plane– Example ax blade for splitting wood

– It turns a downward force into two forces directed out to the sides

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Incline Plane Family

• A screw looks like a spiral incline plane.– It is actually an incline plane wrapped

around a cylinder

– Examples include a spiral staircase and jar lids

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Practice problems

• A roofer needs to get a stack of shingles onto a roof. Pulling the shingles up manually used 1549 N of force. Using a system of pulleys requires 446 N. What is the mechanical advantage?

Mechanical advantage = output force

input force

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Practice problems

• A roofer needs to get a stack of shingles onto a roof. Pulling the shingles up manually used 1549 N of force. Using a system of pulleys requires 446 N. What is the mechanical advantage?

Mechanical advantage = output force

input force

= 1549 N = 3.47

446 N

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• Practice problems

1) Asks for output force (N)

2) Asks for input distance (cm)

3) Asks for output force (N)

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• #1

444.4N

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• #2

11cm

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• #3

3 675N

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4) Asks for output distance (cm)

5) Asks for input force (N)

6) Asks for output distance (m)

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• #4

3/0.85= 3.52

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• #5

2220/.0893= 24 860N

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• #6

1.57/12.5=0.1256m

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Help Solve for MA in #7 & #8

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• #7

3.28

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• #8

23.99

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Compound Machines

• Compound machines are machines made of more than one simple machine– Example include a pair of scissors has 2

first class levers joined with a common fulcrum; each lever arm has a wedge that cuts into the paper

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Energy

• Energy is the ability to cause changes.

– It is measured in Joules or kg●m/s2

– When work is done on an object, energy is given off

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Energy

5 main forms of energy:

1. Mechanical – associated with motion

2. Heat – internal motion of atoms

3. Chemical – the energy required to bond atoms together

4. Electromagnetic – movement of electric charges

5. Nuclear – released when nuclei of atoms fuse or split

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Mechanical Energy

• Mechanical Energy is the sum of the kinetic and potential energy of a large-scale objects in a system– Nonmechanical energy is the energy that

lies at the level of atoms and does not affect motion on a large scale

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Energy

• Those 5 forms of energy can be classified into one of two states:

– Potential energy – stored energy

– Kinetic energy – energy in motion

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Kinetic Energy

• The energy of motion

• An object must have mass and be moving to possess kinetic energy– The greater the mass or velocity--- the

greater the kinetic energy

– Formula:

KE = ½ mv2

m = mass

v = velocity

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Kinetic Energy

• Atoms and molecules are in constant motion and therefore have kinetic energy– As they collide then the kinetic energy is

transferred from one to another

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Practice problem

A sprinter runs at a forward velocity of 10.9 m/s. If the sprinter has a mass of 72.5 kg. What is their kinetic energy?

KE = ½ mv2

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Practice problem

A sprinter runs at a forward velocity of 10.9 m/s. If the sprinter has a mass of 72.5 kg. What is their kinetic energy?

KE = ½ mv2

= ½ (72.5 kg) (10.9 m/s)2

= .5 x 72.5 x 118.81

= 4306.86 kg●m/s = 4306.86 J

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Potential Energy

• The stored energy that a body possesses because of its position. – Examples: chemical energy in fuel or food

or an elevated book because it has the potential to fall.

• Potential energy due to elevated potential is called gravitational potential energy (GPE).

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Potential energy

• Formula:

• PE = mghm = mass

g = gravity (9.8 m/s2)

h = height

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Practice problems

A pear is hanging from a pear tree. The pear is 3.5 m above the ground and has a mass of 0.14 kg. What is the pear’s gravitational potential energy?

PE = mgh

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Practice problems

A pear is hanging from a pear tree. The pear is 3.5 m above the ground and has a mass of 0.14 kg. What is the pear’s gravitational potential energy?

PE = mgh

= .14 kg x 9.8 m/s2 x 3.5 m

= 4.8 kg●m2/s2 = 4.8 J

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Conservation of Energy

• Energy is almost always converted into another form of energy

• One most common conversion is changing from potential energy to kinetic energy or the reverse.

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Conservation of Energy

• The transfer of energy from one object to the next is a conversion of energy.

The law of conservation of energy states that all energy

can neither be created or destroyed; it is just converted

into another form.

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Conservation of Energy

• Energy conversions occur without a loss or gain in energy

• Therefore…. KE = PE

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Energy Transformations

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Conservation of Energy

• Amount of energy the machines transfers to the object cannot be greater than energy you put in

• Some energy is change to heat by friction

• An ideal machine would have no friction so energy in = energy out

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Efficiency

• Efficiency is a measure of how much work put into a machine is changed to useful work output by the machine

• Not all work done by a machine is useful therefore we look at the efficiency of the machine

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Efficiency

• Formula for Efficiency

• (Work output / Work input) X 100– Efficiency = useful work output x 100

work input

• Efficiency is always less than 100% because no machine has zero friction or 100% efficiency

• Lubricants can make a machine more efficient by reducing friction– Oil

– Grease

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Practice Problem

What is the efficiency of a machine if 55.3 J of work are done on the machine, but only 14.3 J of work are done by the machine?

Efficiency = useful work output

work input

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Practice Problem

What is the efficiency of a machine if 55.3 J of work are done on the machine, but only 14.3 J of work are done by the machine?

Efficiency = useful work output

work input

= 14.3 J x 100 = 25.9 %

55.3 J

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Perpetual Motion Machines

• Perpetual motions machines are machines designed to keep going forever without any input of energy

• It is not possible because we have not been able to have a machine with a complete absence of friction!

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• Newman’s machine

Joseph Newman, claimed it would produce mechanical power exceeding the electrical power being supplied to it

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• Take out your homework

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Power, Work and Force I

1. 6.48W

2. 6 692J

3. 5.76S

4. 112.93 kg

5. 7.11W

6. 16.4S

7. 9.45W

8. 1.8kg

9. 61.25W

10. 11 340J

11. 4344.6W

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Work and Power I

1. 20J

2. 5 900J

3. 14 000J

4. 50m

5. 5.10m

6. 50W

7. 13W

8. 18 000J

9. 100J

10. 60W

11. 588W

12. 5000W

13. 115N in 15m(1725J

14. 20kg lift=1960J

15. 80%

16. 500J

17. over 490J

18. What do you think?

19. 25%