Work, Power, and Machines Physical Science – Unit 7 Chapter 9.

transcript

Work, Power, and Machines

Physical Science – Unit 7

Chapter 9

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

– Using a hammer

– Running up a ramp

• 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

– 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

• kJ = kilojoules = thousands of joules

• MJ = Megajoules = millions of joules

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

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

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.

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

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?????

F = ma

= 3.2 kg x 3.2 m/s2

= 10.2 kg● m/s2 = 10.2 N

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

Get a calculator

W= F x D

2.398m

W= F x D

2 800 000N

900 000N

95 454N

W= F x D

237 825J

3.2 x 106 J

5 625 000 J

2 127 840J

• Calculate force first, then work

276 115J

– 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

Power = work

P = W/t

• SI units for power – watts (W)

• 1 kW – Kilowatt = 1000 watts

• 1 MW – Megawatt= 1 million watts

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

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

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

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

1st convert 8 hr to seconds

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

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

• P58 asks for work

P= W/t

412.5J

1 710 000J

7 500 000 J

1.17 x 1010J

955.36 sec

456.14sec

1 500sec

4.5sec

5 x 108 watts

2.75 x 1010

300sec

6 162 000J

• 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.

• 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!

• 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.

• 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)

• 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

• Mechanical advantage = output force

input force

• Mechanical advantage= input distance

output distance

Simple Machines

Lever Pulley Wheel & Axle

Inclined Plane Screw Wedge

• 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

– Resistance/load in middle

– Effort in middle

• Pulley– grooved wheel with a rope or chain

running along the groove

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

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

IMA = 0 IMA = 1 IMA = 2

• Fixed Pulley

IMA = 1

does not increase force

changes direction of force

• Movable Pulley

IMA = 2 increases forcedoesn’t change direction

• Block & Tackle

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

• 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 and Axle

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

• 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.

• MA=Length/Height

• 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

• 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

• 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

• 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

2) Asks for input distance (cm)

3) Asks for output force (N)

444.4N

3 675N

5) Asks for input force (N)

6) Asks for output distance (m)

3/0.85= 3.52

2220/.0893= 24 860N

1.57/12.5=0.1256m

• 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

• 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

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

• 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

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

– Potential energy – stored energy

– Kinetic energy – energy in motion

• 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

• 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

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

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

• 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).

• Formula:

• PE = mghm = mass

g = gravity (9.8 m/s2)

h = height

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

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

• 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.

The law of conservation of energy states that all energy

can neither be created or destroyed; it is just converted

into another form.

• Therefore…. KE = PE

• Some energy is change to heat by friction

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

• 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

• 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

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

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

• 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!

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

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

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%

Work, Power, and Machines Physical Science – Unit 7 Chapter 9.

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