Download Work, Energy, and Power

Work, Energy and Power!
James Joule
•The metric system unit of energy is the joule (J),
after James Joule.
•Energy-ability to do work
Mechanical
• Mechanical energy is the energy which
is possessed by an object due to its motion
or its stored energy of position
• Kinetic energy : is the energy of motion
• Potential Energy : an object can store energy
as the result of its position
Work Concept
• Work is defined as a force acting upon an
object to cause a displacement
• Mathematically, work can be expressed by
the following equation.
• W= F x d cos q ( cos 00 = 1)
• where F = force, d = displacement, and the
angle (theta) is defined as the angle between
the force and the displacement vector
Condition for work
• The force and displacement must be in the
same direction for positive work to be done
(or at least a component of the force)
• W= F x d cos q ( cos 00 = 1)
Garcon does work when
he picks up the tray
but not while he
carries it around
the room
Work Calculations
W=F x d
W=F x d cos 300
W= F x d
=100N X 5m = 100N X 5m X .87
=15kg(9.8m/s2) X 5m
=500 N m
= 735 N m
= 433 N m
Gravitational Potential Energy
• After an object has been lifted to a
height, work is done.
•
PE = W= F x d= mgh
Potential Energy is
maximum at the
maximum HEIGHT
Potential Energy Calculation
• How much potential energy is lost by a
5kg object to kinetic energy due a
decrease in height of 4.5 m
• PE = mgd
• PE = (5kg)(9.8 m/s2)(4.5 m)
• PE = 225 kg m2/s2
• PE = 221 J
Kinetic Energy Calculation
• The energy of motion
KE =1/2 mv2
• Find the kinetic energy of an 4 kg object
moving at 5m/s.
• KE = 1/2 mv2
• KE = ½ (4kg)(5m/s) 2
• KE = 50 kg m 2 /s 2
• KE = 50 J
Working off that jelly donut
A jelly donut has about 1
million joules of stored
chemical energy in it. How
high would a 50-kg person
have to climb to work off that
jelly donut?
Work = change in KE
• This is called:
the Work-Energy Theorem
• Work = K1 – K0
•
Work =
2
1/2mv
–
2
1/2mvo
• A .023kg bullet is accelerated in a rifle
barrel 56.1 cm long to a speed of 363 m/s
from rest.
• Use the work-energy theorem to find the
average force exerted on the bullet while it
is being accelerated.
• A forklift raises a box 1.2 m doing 7.0 kJ of
work on it. What is the mass of the box?
• A rope is used to pull a metal box 15.0 m
across the floor. The rope is held at an
angle of 46.0˚ with the floor and a force of
628N is used. How much work does the
force do on the rope?
• An airplane passenger carries a 215N
suitcase up the stairs, a displacement of 4.20
m vertically.
• How much work does the passenger do?
• Then the passenger carries the suitcase
down the same stairs. How much work is
done?
Work = change in KE
• A rifle can shoot a 4.2 g bullet at a speed of
965 m/s.
• Find the kinetic energy of the bullet as it
leaves the rifle.
• What work is done on the bullet if it starts
from rest?
• If the work is done over .75 m, what is the
average force on the bullet?
Work = change in KE
• An 875-kg compact car speeds up from 22.0
m/s to 44.0 m/s while passing another car.
• Calculate its initial and final energies.
• How much work was done to increase its
speed?
Kinetic Energy of your car
• A car is going 55
mph, using the
formula for K = ½
mv2, estimate how
much more energy
is required to reach
75 mph? (car mass
is 1000 kg)
More Work =∆KE
• Some driver's license exams have the
following question.
• A car moving 50 km/hr skids 15 meters
with locked brakes. How far will the car
skid with locked brakes (assuming the force
of the brakes is the same in both situations)
if it is moving at 150 km/hr?
Power!
•
•
•
•
Power is the rate that we use energy.
Power = Work or Energy / Time
P = W/t = F x d/t = F v
The units for power :
• J/s or Watts
Power Calculation
• A 5 kg cart is pushed by a 30 N force
against friction for a distance of 10 m in 5
seconds. Determine the Power needed to
move the cart.
• P=Fxd/t
• P = 30 N (10 m) / 5 s
• P = 60 watts
Power II
A box that weighs 575 N is lifted a distance
of 20.0 m straight up by a cable attached to
a motor. The job is done in 10.0s. What
power is developed by the motor in Watts?
Power practice III
• How long would a 200 W lightbulb have to
glow to produce 1456 J of energy?
Power = Work/time
• An electric motor develops 65kW of power
as it lifts a loaded elevator 17.5 m in 35s.
How much force does the motor exert?
Summary
• Energy is the ability to do work
• Potential is stored energy (Statics)
• Dependent on height
• Kinetic is moving energy (Dynamics)
• Dependent on velocity