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Work and Energy

- Chapter 5

Work

- Work is defined in physics as the product of the

magnitudes of the component of a force along the

direction of displacement and the displacement. - Work force distance
- W Fd
- Work is not done on an object unless the object

is moved due to the action of a force. - Work is done only when components of a force are

parallel to a displacement. - Components of the force perpendicular to a

displacement do no work. - Work has dimensions of force times length.
- In the SI system work is Nm Joules

Energy

- Energy is the most central concept underlying all

of science. - Energy is spent when we lift a load against

Earths gravity. The heavier the load or the

higher we lift, the more work we do. - Work is a type of energy that is defined as

force x distance. - Two things enter in every case where work is done
- 1. The application of a force
- 2. The movement of something by that force.
- W f d
- The unit of measurement of work is Nm Joule
- One Joule of work is done when a force of 1N is

exerted over a distance of 1 meter.

Work

F

?

d

- Imagine that you push a crate along the ground.

If the force that you exert on the crate is

horizontal, all of your effort moves the crate. - If your force is other than horizontal, only the

horizontal component of your applied force causes

a displacement and does work. - If the angle between the force and the direction

of the displacement is ?, work can be written as

follows - W F cos ? d
- Net work net force cosine of the

angledisplacement

WorkExample 1 Panchito is raised 6 m above a

platform by Kelly using a conveyor belt.

Panchitos mass is 70 kg. How much work is done

on Panchito?

- Given m 70 kg , d 6 m a -9.81 m/s²
- Unknowns F, W
- Solution
- F ma
- Fg (70 kg) (-9.81 m/s²)
- Fg -686.7 kgm/s²
- F 687 N
- W Fd
- W (687 N) (6 m)
- W 4,122 Nm
- W 4,122 J

Example 2 Find the work done on a box that was

pushed 5 m by a Force of 50 N at an angle of 30

below the horizontal. The mass of the box is 5

Kg.

Fn

30

50 N

Fg

? x d 5 m

Example 2Find the work done on a box that was

pushed 5 m by a Force of 50 N at an angle of 30

below the horizontal. The mass of the box is 5

Kg.

- Given F 50 N m 5 kg d 5 m
- ? 30
- Solution
- W F d cos ?
- W (50 N) (5m) (cos 30)
- W 216.51 Joules

30

60º

30º

d

Physics

Problem Set 19

October 31, 2007Student Name

_________________________

Class Period ___

- 1. A flight attendant pulls her 70 N flight bag a

distance of 253 m along a level airport floor at

a constant speed. The force she exerts is 40 N at

an angle of 53 above the horizontal. - A) Find the work that she does on the flight bag

Answer __________

- B) Find the work done by the force of friction on

the bag

Answer __________ .

- - 2. Yogi Berra, from the New York Yankees was the

best catcher that ever played the game. As he

often caught the baseball, he would gave in so

that his glove was displaced 10 cm with a force

of 525 N from the pitcher. How much work is done

by the ball? -

Answer __________

40 N

53

Bonus Points

- P/1 If ½ is ¾ of 4/5 of a certain number.
- What is the number?

Work and Energy

Energy

- We study primarily two different forms of energy
- Potential Energy
- Kinetic Energy
- Potential Energy
- is also known as stored energy
- It describes an object that has to move because

of its position with respect to some other

location

Potential Energy

- Is also known as stored energy
- The SI unit for Potential Energy is the Joule
- It describes an object that has the potential to

move because of its position with respect to some

other location. - The energy associated with an object due to the

objects position relative to a gravitational

source is called gravitational potential energy - PEg m g h

Potential Energy Example 1 Juan went to the

top of the roof at his High School. Juan has a

mass of 41 kg.If the height of the roof is 15 m,

calculate Juans Potential Gravitational Energy

to the ground.

- Given h 15 m g 9.81 m/s² m 41 kg
- Unknown PEg ?
- PEg mgh
- PEg (41 kg) ( 9.81 m/s²) ( 15 m)
- PEg 6,033.15 J

Kinetic Energy

- Is energy associated with an object in motion
- Kinetic energy depends on the speed of the

object. - Kinetic energy depends on the mass of the

objects. (bowling ball vs volleyball going at the

same speed) - KE ½ mv²

Kinetic EnergyExample 1 A 6 kg bowling ball

moves at 4 m/s.a) How much kinetic energy does

the bowling ball have?b) How fast must a 2.5 kg

tennis ball move in order to have the same

kinetic energy as the bowling ball?

- Given mb 6 kg vb 4 m/s mt 2.5 kg
- Unknown KE ?
- Solution KE ½ mb vb²
- KE ½ (6 kg) (4 m/s)²
- KE 48 J
- KE ½ mt vt²
- vt v2 KE/mt 6.20 m/s

Conservation of EnergyPower

- Chapter 5

Conservation of Energy

- When we say that something is conserved it means

that it remains constant, it doesnt mean that

the quantity can not change form during that

time, but it will always have the same amount. - Conservation of Mechanical Energy
- MEi MEf
- initial mechanical energy final mechanical

energy

Conservation of Energy

- If the only force acting on an object is the

force of gravity - KEi PEi KEf PEf
- ½ mvi² mghi ½ mvf² mghf

Conservation of Mechanical EnergyExample

1Kelly zooms down a frictionlesswith an

initial height of 3 m. Kellys mass is 25 kg.

What is her speed at the bottom of the?

3 m

Conservation of Mechanical EnergyExample

1Kelly zooms down a frictionlesswith an

initial height of 3 m. Kellys mass is 25 kg.

What is her speed at the bottom of the?

- Given hi 3 m m 25 kg vi 0 m/s
- hf 0 m

Power

- Chapter 5

Power

- Power is the rate at which work is done.
- Power is the rate of energy transfer by any

method. - The SI unit of power is the watt, W
- 1 watt 1 Joule/s
- 1000 watts 1 kW

Power

- Power Work / time
- Work force distance
- Power forcedistance/time
- Power forcevelocity
- P Fv

PowerExample 1 A 200 kg curtain needs to be

raised 8m. in as close to 5 s as possible. You

need to decide among three motors to buy for

this, each motor cost a little more the bigger

the power rating.The power rating for the three

motors are listed as 1.0 kw, 3.5 kw and 5.5 kw.

Which motor is the best for the job?

- Given m 200 kg d 8 m ?t 5s
- Unknown Power and work
- Solution Find the work done first and then

divide by the time to get the power. - W Fd
- W mgd
- W (200 kg)(9.81 m/s²)(8 m)
- W 15,696 Joules
- P W/?t
- P 15,696 J / 5 s
- P 3,139 watts

Work-Kinetic Energy Theorem

- The net work done on an object is equal to the

change in the kinetic energy of the object. - Wnet ?KE

PowerExample 2A 1,200 kg elevator carries a

maximum load of 900 kg. A constant frictional

force of 400 N retards the elevators motion

upward.What minimum power, in kilowatts must the

motor deliver to lift the fully loaded elevator

at a constant speed of 4 m/s?

PowerExample 3A 1,500 kg car accelerates

uniformly from rest to 10 m/s in 3 sa) What is

the work done on the car in this time

interval?b) What is the power delivered by the

engine in this time interval?

Physics

Problem Set 21 Nov/27/07

Student Name _________________________________

Class Period ________

(No Transcript)

Physics Problem Set

21 Nov/01/05 Student Name _____________________

___ Class Period ________

- 1. Alyssas car accelerates uniformly from rest

to 10 m/s in 3 s. Allyssa and her car have a

combined mass is 1600 kg. - What is the work done on the car in this time

interval? - Given vi 0 , vf 10 m/s , ?t 3 s m

1,600 kg - Unknowns W, F, a, ?x
- Solution a ?v/ ?t vf-vi/ ?t 10m/s 0

m/s / 3s 3.33 m/s² - F ma (1,600 kg) (3.33 m/s²) 5,328 N
- W F d
- d ? ? ?x vi(?t)

½ a (?t)² - ?x

0 ½ (3.33 m/s²)(3s)² 14.99 m - W F d (5,328 N) (14.99 m) 79,867 J
- B) what is the power delivered by the engine in

this time interval? - P W/t 79,867 J / 3s 26622

Watts

- 2. Erikas car accelerates uniformly from rest to

13 m/s in 2 s. Erika and her car have a combined

mass is 1,550 kg. - What is the work done on the car in this time

interval? - F (1,550 kg) (13 m/s / 2s)

10,075 N - ?x ½ (6.5 m/s²)(2s)² 13 m
- W Fd (10,075 N) (13m)

130,975 J - B) what is the power delivered by the engine in

this time interval? - P W/?t 130,975 J/ 2s 65,488 Watts
- 3. A 1000 kg elevator carries a maximum load of

800 kg. A constant frictional force of 4000 N

retards the elevators motion upward. What

minimum power, in kilowatts, must the motor

deliver to lift the fully loaded elevator at a

constant speed of 3 m/s ? - Given m 1,000 kg 800 kg 1,800 kg
- Fk 4,000 N
- v 3 m/s
- Unknown P
- Solution P F v (Fg Fk)

v (mg Fk) v

- 4. A rain cloud contains 2,660,000 kg of water

vapor. How long would it take for a 2 kW pump to

raise the same amount of water to the cloud

altitude of 2 km? - Given m 2,660,000 kg
- P 2 kW ? P 2,000 Watts
- d 2 km ? d 2,000 m
- Unknown ?t, W
- Solution W Fd (mg)d (2,600,000 Kg)

(9.81 m/s²) (2,000 kg) - W 51,012,000,000 J
- P W/?t ? ?t W/P
- ?t

51,012,000,000 J/ 2,000 Watts - ?t 25,506,000 s (about 8.27

years)

Physics

Problem Set 13

Monday Dec. 5, 2005Student name

___________________________________

Class Period _____

Physics Problem Set 14 Tuesday Dec.6,

2005 Student Name _________________________

Class Period _____

- 1 A 5.60 kg rubber ball has a speed of 3 m/s at

point A and a kinetic energy of 7.5 J at point B.

Determine the following - a) The ball kinetic energy at point A

________ - b) The ball speed at point B

________ - c) The total work done on the ball as it

moves from A to B

________ - Erica threw a ball that has a mass of 3.50 kg.

The initial speed of the ball was - 12 m/s at point A and a kinetic energy of 19.5 J

at point B. Determine the following - a) The ball kinetic energy at point A

________ - b) The ball speed at point B

________ - c) The total work done on the ball as it moves

from A to B ________ - Starting from rest, a 20 kg suitcases 5 m.

down a frictionless ramp inclined at a 40 angle

from the floor. The suitcase thens an

additional 8 m. until it comes to a stop.

Determine the following - The speed of the suitcase at the bottom of the

ramp. ________ - The coefficient of kinetic friction between the

suitcase and the floor ________ - The mechanical energy lost due to friction

________ - 4 A skier of mass 60 kg is pulled up a slope by a

motor-driven cable. How much work is required to

pull the skier 60 m up a 30 slope (assumed to be

frictionless) at a constant speed of 3 m/s?

________

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