Transcript Work and Energy

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 = F·d
• 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 N·m = Joules
Energy
• Energy is the most central concept underlying all of science.
• Energy is spent when we lift a load against Earth’s 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=fd
• 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
ө
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 ө, work can be written as follows:
W = F cos ө · d
Net work = net force ·cosine of the angle·displacement
Work
Example 1: Panchito is raised 6 m above a platform by
Kelly using a conveyor belt. Panchito’s 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= m·a
Fg = (70 kg) (-9.81 m/s²)
Fg = -686.7 kg·m/s²
F = 687 N
W = F·d
W = (687 N) (6 m)
W = 4,122 N·m
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.
30 °
Fn
Fg
∆x=d=5m
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.
• Given: F = 50 N
•
ө = 30°
m = 5 kg
d=5m
30°
60º
30º
d
• Solution:
W = F d cos ө
W = (50 N) (5m) (cos 30°)
W = 216.51 Joules
Physics
Problem Set # 19
Student Name : _________________________
October 31, 2007
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.
53°
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: __________
3. How much work is done on a vacuum cleaner pulled 5 m by a force of 75 N?
Answer: __________
.
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 object’s 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 Juan’s
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 Energy:
Example # 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 = √2 KE/mt = 6.20 m/s
Conservation of Energy
Power
Chapter 5
Conservation of Energy
• When we say that something is conserved
it means that it remains constant, it doesn’t
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 Energy
Example # 1:
Kelly zooms down a frictionless slide with an initial
height of 3 m. Kelly’s mass is 25 kg.
What is her speed at the bottom of the slide?
3m
Conservation of Mechanical Energy
Example # 1:
Kelly zooms down a frictionless slide with an initial
height of 3 m. Kelly’s mass is 25 kg.
What is her speed at the bottom of the slide?
• 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
Work
Power 
time
Power
Power = Work / time
Work = force · distance
Power = force·distance/time
Power = force·velocity
P = F·v
Power:
Example 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 = F·d
W = m·g·d
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 = ΔKE
Power
Example # 2
A 1,200 kg elevator carries a maximum load of 900 kg.
A constant frictional force of 400 N retards the elevator’s 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?
Power
Example # 3
A 1,500 kg car accelerates uniformly from rest to 10 m/s in 3 s
a) 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: ________
P/1
Sabrina’s car accelerates uniformly from rest to 15 m/s in 3 s. Sabrina and her car have a combined
mass is 1600 kg.
a) What is the work done on the car in this time interval?
Answer: ___________
b) What is the power delivered by the engine in this time interval?
Answer: ___________
P/2
A 1,200 kg elevator carries a maximum load of 900 kg. A constant frictional force of 500 N retards the
elevator’s 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 ?
Answer: ___________
P/3
A 7 kg bowling ball moves at 6 m/s.
a) How much kinetic energy does the bowling ball have?
Answer: __________
b) How fast must a 2.5 kg tennis ball move in order to have the same kinetic energy as the
bowling ball?
Answer: __________
P/4
A ball is at the top of a building 12 m high. The ball has a mass of 2 kg.
A)
Calculate the potential energy of the ball to the ground?
Answer: _________
B) If the ball drops to the ground, what will be its velocity as it hits the ground?
Answer: _________
Physics
Problem Set # 21
Nov/01/05
Student Name: ________________________ Class Period: ________
1. Alyssa’s car accelerates uniformly from rest to 10 m/s in 3 s. Allyssa and
her car have a combined mass is 1600 kg.
A)
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 = m∙a = (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. Erika’s car accelerates uniformly from rest to 13 m/s in 2 s. Erika and her car
have a combined mass is 1,550 kg.
A) 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 = F∙d = (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 elevator’s 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
P = {(1,800 kg)(9.81 m/s²) + 4,000 N }(3 m/s)
P = 64, 974 Watts
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 = F∙d = (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
Student name: ___________________________________
Monday Dec. 5, 2005
Class Period: _____
1 A 0.60 kg rubber ball has a speed of 2 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
________
2 A 2.50 kg rubber ball has a speed of 12 m/s at point A and a kinetic energy of 18.5 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
________
3 Starting from rest, a 10 kg suitcase slides 3 m. down a frictionless ramp inclined at a
30° angle from the floor. The suitcase then slides an additional 5 m. until it
comes to a stop. Determine the following;
a)
The speed of the suitcase at the bottom of the ramp.
________
b)
The coefficient of kinetic friction between the suitcase and the floor ________
c)
The mechanical energy lost due to friction
________
4 A skier of mass 70 kg is pulled up a slope by a motor-driven cable. How much work
is required to pull the skier 60 m up a 35° slope (assumed to be frictionless) at a
constant speed of 2 m/s?
________
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
________
2
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
________
3
Starting from rest, a 20 kg suitcase slides 5 m. down a frictionless ramp inclined at
a 40° angle from the floor. The suitcase then slides 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
________
a)
b)
c)
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?
________