General Physics 1: Work_ Energy_ and Power.ppt

Calculations of work, power and energy

1. Work, Energy and Power!Work, Energy and Power!
The Calculations and
Equations

2. Energy and Work
•Energy is the ability to do work.
•Work is the energy transferred to
or from a system by a force that
acts on it.

3. MechanicalMechanical
•Mechanical energyMechanical energy is the energy which is the energy which
is possessed by an object due to its motion is possessed by an object due to its motion
or its stored energy of positionor its stored energy of position
• Kinetic energy :Kinetic energy : is the energy of motion is the energy of motion
• Potential EnergyPotential Energy : : an object can store energy an object can store energy
as the result of its position or elastic source as the result of its position or elastic source

4. WorkWork
•In physics, In physics, workwork has a has a
very specific very specific
meaning. meaning.
•In physics, work In physics, work
represents a represents a
measurable changemeasurable change in in
a system, caused by a a system, caused by a
force.force.

5. Work ConceptWork Concept
•WorkWork is defined as a force acting upon an is defined as a force acting upon an
object to cause a displacement object to cause a displacement
•Mathematically, work can be expressed by Mathematically, work can be expressed by
the following equation.the following equation.
• W= F x d cos W= F x d cos  cos 0 cos 0
00
= 1) = 1)

•where F = force, d = displacement, and the where F = force, d = displacement, and the
angle (theta) is defined as the angle between angle (theta) is defined as the angle between
the force and the displacement vectorthe force and the displacement vector

6. Work (force is parallel to distance)Work (force is parallel to distance)
W = F x d
Distance (m)
Force (N)
Work (joules)

7. Work (force at angle to distance)Work (force at angle to distance)
W = Fd cos (q)
Distance (m)
Force (N)
Work (joules) Angle

8. Work CalculationsWork Calculations
W=F x d W=F x d cos 30
0
W= F x d
=100N X 5m = 100N X 5m X .87 =15Kg(10m/s
2)
X
5m
=500 N m = 413 N m = 750 N m

9. Gravitational Potential EnergyGravitational Potential Energy
•After an object has been lifted to a After an object has been lifted to a
height, work is done.height, work is done.
• PE = W= F x d= mghPE = W= F x d= mgh
Potential Energy
is maximum at
the maximum
HEIGHT

10. Potential Energy CalculationPotential Energy Calculation
•How much potential energy is lost by a How much potential energy is lost by a
5Kg object to kinetic energy due a 5Kg object to kinetic energy due a
decrease in height of 4.5 mdecrease in height of 4.5 m
•PE = mghPE = mgh
•PE = (5Kg)(10 m/sPE = (5Kg)(10 m/s
22
)(4.5 m))(4.5 m)
•PE = 225 Kg mPE = 225 Kg m
22
/s/s
2 2
•PE = 225 JPE = 225 J

11. Kinetic Energy CalculationKinetic Energy Calculation
•The energy of motionThe energy of motion
KE = W= F x d= mgh=1/2 mvKE = W= F x d= mgh=1/2 mv
22
•Find the kinetic energy of an 4 Kg object Find the kinetic energy of an 4 Kg object
moving at 5m/s.moving at 5m/s.
•KE = 1/2 mvKE = 1/2 mv
22
•KE = ½ (4Kg)(5m/s) KE = ½ (4Kg)(5m/s)
22
•KE = 50 Kg m KE = 50 Kg m
22
/s /s
22
•KE = 50 JKE = 50 J

12. Elastic potential energy Elastic potential energy

13. Spring constant CalculationSpring constant Calculation
A tired squirrel (mass of 1 kg) does push-
ups by applying a force to elevate its
center-of-mass by 5 cm. (A) Determine the
number of push-ups which a tired squirrel
must do in order to do a mere 5.0 Joules of
work. (B) Determine the squirrel’s spring
constant.

14. Spring Constant CalculationSpring Constant Calculation
•W = F x d = 10 N*(.05m)=.5 N m W = F x d = 10 N*(.05m)=.5 N m
• W = .5 J (each push up)W = .5 J (each push up)
• 10 pushups = 5 J10 pushups = 5 J
• PE = ½ k x PE = ½ k x
22
•.5 J = ½ k (.05m) .5 J = ½ k (.05m)
22
•.5 J = ½ k (.003m .5 J = ½ k (.003m
22
))
•.5 J = .0015 m .5 J = .0015 m
2 2
•333.3 J/m 333.3 J/m
2 2
= k= k

15. Power!Power!
•Power is the rate that we use energy.Power is the rate that we use energy.
•Power = Work or Energy / TimePower = Work or Energy / Time
•P = W/t = F x d/t = F vP = W/t = F x d/t = F v
•The units for power :The units for power :
•J/sJ/s
•Kg mKg m
22
/ s / s
2 2
/s/s
•N m / sN m / s

16. Spring 2008 16
PowerPower
•Power is simply energy exchanged Power is simply energy exchanged
per unit time, or how fast you get per unit time, or how fast you get
work done (Watts = Joules/sec) work done (Watts = Joules/sec)
•One horsepower = 745 WOne horsepower = 745 W
•Perform 100 J of work in 1 s, and Perform 100 J of work in 1 s, and
call it 100 Wcall it 100 W
•Run upstairs, raising your 70 kg Run upstairs, raising your 70 kg
(700 N) mass 3 m (2,100 J) in 3 (700 N) mass 3 m (2,100 J) in 3
seconds seconds  700 W output! 700 W output!
•Shuttle puts out a few GW Shuttle puts out a few GW
(gigawatts, or 10(gigawatts, or 10
99
W) of power! W) of power!

17. Spring 2008 17
More Power ExamplesMore Power Examples
•Hydroelectric plantHydroelectric plant
•Drops water 20 m, with flow rate of 2,000 mDrops water 20 m, with flow rate of 2,000 m
33
/s/s
•1 m1 m
33
of water is 1,000 kg, or 9,800 N of weight (force) of water is 1,000 kg, or 9,800 N of weight (force)
•Every second, drop 19,600,000 N down 20 m, givingEvery second, drop 19,600,000 N down 20 m, giving
392,000,000 J/s 392,000,000 J/s  400 MW of power 400 MW of power
•Car on freeway: 30 m/s, Car on freeway: 30 m/s, AA = 3 m = 3 m
22
 FF
dragdrag1800 N1800 N
•In each second, car goes 30 m In each second, car goes 30 m  WW = 1800 = 180030 = 54 kJ30 = 54 kJ
•So power = work per second is 54 kW (72 horsepower)So power = work per second is 54 kW (72 horsepower)
•Bicycling up 10% (~6Bicycling up 10% (~6º) slope at 5 m/s (11 m.p.h.)º) slope at 5 m/s (11 m.p.h.)
•raise your 80 kg self+bike 0.5 m every secondraise your 80 kg self+bike 0.5 m every second
•mghmgh = 80 = 809.89.80.5 0.5  400 J 400 J  400 W expended 400 W expended

18. Power CalculationPower Calculation
•A 5 Kg Cart is pushed by a 30 N force against A 5 Kg Cart is pushed by a 30 N force against
friction for a distance of 10m in 5 seconds. friction for a distance of 10m in 5 seconds.
Determine the Power needed to move the cart.Determine the Power needed to move the cart.
•P = F x d / tP = F x d / t
•P = 30 N (10 m) / 5 sP = 30 N (10 m) / 5 s
•P = 60 N m /sP = 60 N m /s
•P = 60 wattsP = 60 watts

19. SummarySummary
•Energy is the ability to moveEnergy is the ability to move
•Potential is stored energy (Statics)Potential is stored energy (Statics)
•Dependant on heightDependant on height
•Kinetic is moving energy (Dynamics)Kinetic is moving energy (Dynamics)
•Dependant on velocityDependant on velocity
•Springs store energy dependant on distance and Springs store energy dependant on distance and
constantconstant
•Power is how fast the work is donePower is how fast the work is done