9 Energy Energy can change from one form to another without a net loss or gain.
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Transcript of Chapter 6. Energy is “conserved” meaning it can not be created nor destroyed Can change form...
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