ENERGY AND ENERGY TRANSFERChapter 6

ENERGY IS CONSERVED

Energy is “conserved” meaning it can not be created nor destroyed Can change formCan be transferred

Total energy does not change with time.

ENERGY Forms

Kinetic Energy Potential Energy Heat

Unit: J (Joules) 1J = 1Nm = 1kg m2 / s2

MATH: VECTOR DOT PRODUCT

DOT PRODUCT EXAMPLE

DOT PRODUCT EXAMPLE

WORK BY CONSTANT FORCE

s

F

WF > 0

s

F

WF = 0

s

F

WF < 0

sF

WF > 0

Work means energy transfer.

THE SIGN OF WORKThe angle θ between the force and the displacement determines

the sign of W.

WEIGHTLIFTER WHEN NOT MOVING

WEIGHTLIFTER WHEN LOWERING

FIND THE WORK DONE BY EACH FORCE

θ=20º

ONE-DIMENSIONAL EXAMPLE

A force F = 10 N pushes a box across a frictionless floor for a distance s = 5 m.

s

F

WORK BY CONSTANT FORCE

30°

50 N

WF = F s cos θ =(50N)(5m)cos30o = 216.5 J

You pull a chest (of weight 30N) 5m across the floor at a constant speed by applying a force of 50N at an angle of 30°. How much work have you done?

WHERE DID THE ENERGY GO?You pull a 30 N chest 5m across the floor at a constant

speed, by applying a force of 50 N at an angle of 30°.

How much work did gravity do?

How much work did normal force do?

How much work did friction do?30

50 N

WHAT IS THE FRICTION?

30°

F=50 N

SUMMARY

WF +216.5J

WG 0J

WN 0J

Wf -216.5J

Wtotal 0J

WHERE DID THE ENERGY GO?

You spent 216.5J of energy pulling.

Gravity and normal force absorbed none of the energy.

Friction absorbed all 216.5J of energy.

Negative work done means it absorbs instead of supplying energy.

POSITIVE AND NEGATIVE WORK

If W>0, it means the force gives energy to the object.

If W<0, it means the force absorbs energy from the object.

WHO DOES THE WORK?

Make sure when you calculate the work done W, you know which force you are dealing with.

In general, different force gives different work.

Like in the previous example:

NORMAL FORCE

You are towing a car up a hill with constant velocity. The work done on the car by the normal force is:

1. positive2. negative3. zero

W

T

FN V

GRAVITYYou are towing a car up a hill with constant velocity. The work done on the car by the gravitational force is:

1. positive2. negative3. zero

W

T

FN V

GRAVITYYou are towing a car up a hill with constant velocity. The work done on the car by the gravitational force is:

W

T

FN V

TENSION

You are towing a car up a hill with constant velocity. The work done on the car by the tension force is:

1. positive2. negative3. zero

W

T

FN V

KINETIC ENERGY

If I did 100J of work to push an object of 2kg on a frictionless surface, what KE does it have in the end? Assume the object was initially at rest.

What is the final velocity?

WORK KINETIC ENERGY THEOREM

All this says is that the total work we do on an object goes into its KE.

Note that this is total work done, not just the work of one of the forces. To calculate Wtotal, you need to find the work of all the forces and add them up.

EXAMPLE

Alice and Bob are both pushing a box. Alice does 200J of work, Bob does -150J. What is the change in the KE of the box?

WORK BY CONSTANT FORCE You pull a 30 N chest 5 meters across the floor at

a constant speed by applying a force of 50 N at an angle of 30 degrees. What is the total work done?

30

50 N

TOTAL WORK DONEYou are towing a car up a hill with constant velocity. The total work done on the car by all forces is:1. positive2. negative3. zero

W

T

FN V

TEST 1-5

3/6 Weighs the same as a quiz HW + Lecture notes Format similar to exam More difficult questions than the

quizzes

WORK AND POWER

A 100W (=100J/s) light bulb consumes 100J of energy per second.

POWER OF A CONSTANT FORCE

WORK & POWER

Engine of a jet develops a thrust of 15,000 N when plane is flying at 300 m/s. What is the power of the engine ?

POWER FOR CIRCULAR MOTION

I swing a sling shot over my head. The tension in the rope keeps the shot moving in a circle. How much power must be provided by me, through the rope tension, to keep the shot in circular motion ?

Rope Length = 1mShot Mass = 1 kgAngular frequency = 2 rad/s

v

A) 16 J/s B) 8 J/s C) 4 J/s D) 0J/s

POWER FOR CIRCULAR MOTION

Note that the string expends no power, i.e. does no work. Makes sense ?

By the work – kinetic energy theorem, work done equals change in kinetic energy.

KE = 1/2 mv2, thus since v does not change, neither does KE.

A force perpendicular to the direction of motion does not change speed, v, and does no work.

HORSE POWER AND WATTS

Both measures power

1hp = 746W

KILOWATT-HOUR AND JOULES

Both measure energy

1kWh is the amount of energy dissipated by a 1000 Watts light bulb in one hour.

Therefore:

1kWh = (1000J/s) (3600s)=3.6 × 106 J