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WORK
Has a different meaning in PHYSICS
chapter 6
work and energy
WORK
(don’t write this down yet)
Work = Force x displacement
Force
Displacement
WORK
In physics work is:
The force times displacement
W=Fd
displacement traveled
by the object (m)
Dx or Dy or …
Component of force
parallel to the direction motion (N)
Work = F d
N
Nm
m
For work this is
called a Joule (J)
Or
kg m2 If you prefer
s2
A person drags a crate horizontally
across a floor with a force of 30.0 N for a
distance of 5.0 m. (watch signs)
How much work is done on the box?
What
Twice
the distance??
Whatififititwas
waspulled
pulledfor
with
TWICE
the FORCE for
TWICE the DISTANCE??
What if the crate is traveling to the left for
5.0 m and the person exerts a force to
the right of 30.0 N (he is slowing it down).
(watch signs)
How much work does he do on the box?
If the force and displacement are pointed
the same way the work is positive
+ W = (+F) (+d)
+ W = (–F) (-d)
Work itself is not a vector, but its sign does mean something
If the force and displacement are pointed
in opposite directions the work is negative
- W = (+F) (-d)
- W = (–F) (+d)
How much work does a weightlifter do on a a
150 kg barbell lifting set of weight it 1.8 m from
the ground (at a constant velocity)
W=Fd
How much work does a weightlifter do holding
a 150 kg set of weights motionless over his
head for 10 seconds?
Is he exerting a force?
W=Fd
0
How much work is done on a golf ball flying
through space at a constant 220 m/s if it travels
10 m?
W=Fd
0
In order for work to be done, there must
be force AND distance!!
Work = Force x Distance
Lastly in order to count as “work”,
the force has to be in the parallel with the
displacement of the object
The force does work on the box
displacement
Work = Force x Distance
Does this force do work on the box?
Force
displacement
rce
Work = Force x Distance
Work is not done by the force
Only Part of this force will do work
Force
distance
A crate is pulled at a constant velocity with
a force of 130 N by a rope which is 25o
above the horizontal for 8.0 m. How much
work is done.
130 N
25o
8.0 m
How much work is do you do carrying a
20 kg box across a level floor for 10 m at a
constant velocity?
Displacement
Force
In order for work to be done, there must
be force AND distance!!
AND the force has to be in the same
direction as the movement
How much work does Sisyphus do pushing a 540 kg
boulder 1100 m along the slope of a a mountain with
a 65 degree grade? The boulder moves with a
constant velocity up the hill. Ignore friction here
Direction of motion?
Forces in same direction?
How much force does Sisyphus have to exert?
1100 m
FN
540 kg
Fg
65o
Fgx
Force and displacement
are in the same direction
Positive work
Force and displacement
have opposite directions
Negative work
Force and displacement
are perpendicular
zero work
Object is not moving
zero work
Not all forces remain constant as an object moves.
Such as….
Lifting a rocket into space
Pushing on a spring
Pulling two magnets apart etc…..
Here force applied to an object increases linearly
as it moves. The distance is .050 m.
What force would be used.
THE AVERGE FORCE
22 N
Force
0N
0m
Distance
.050 m
W = F d = ½ * 22 *.05
22 N
Force
The AREA
under the
curve
0N
0m
Distance
.050 m
If the force was non-linear, you can break it up into a
bunch of small pieces to find the area under the curve.
22 N
Force
0N
0m
Distance
.050 m
A ball with a mass of 1 kg rotates in a horizontal
circle due to a string with a length of 12 cm
exerting a force of 58 N . How much work does
the string do one the ball in one rotation?
Honors Physics
WS 6-1
What is the
common theme
ENERGY
is the ability to do work.
ENERGY has many forms
2 Main types of ENERGY
Kinetic Energy (KE) – motion
Potential Energy(PE) – position
Both kinetic and potential energy are
considered Mechanical Energy
ENERGY
The ability to do work
It has the same units as work
J
Joule
2
kg m
s2
Work = DENERGY
BIG IDEA!!!!!
Objects with kinetic energy can do work!
When the car hits the wagon, it
exerts a force on the crate
force
distance
Objects with kinetic energy can do work!
force
distance
mass of object (kg)
velocity of object (m/s)
K=
2
mv
2
Kinetic Energy
of the object
Which has a bigger impact on KE,
Mass or velocity?
What is the kinetic energy of a 750 kg car,
traveling at 10 m/s?
Compare KE between
1 kg object moving at 1 m/s
2 kg object moving at 1 m/s?
Compare KE between
1 kg object moving at 1 m/s
1 kg object moving at 2 m/s?
It requires work to give an object kinetic energy.
The more work that is done on the car, the faster it
goes and the more kinetic energy it has
Force
Displacement
How much work is done to speed up a car
mass = m. In the scenario below
V1
V2
Force
Displacement
mass = m
Initial Velocity = v1
Final Velocity = v2
distance of acceleration = d
W=?
F=ma
W=Fd
plugging in gives
W=mad
mass = m
Initial Velocity = v1
Final Velocity = v2
distance of acceleration = d
W=?
W=mad
What equation relates a,d, v1, v2 ,
2
2
v2 = v1 + 2ad
Notice that
W = mad
2
2
v2 = v1 + 2ad
Solving for ad
ad = v2 – v1
2
2
2
W = mad
ad = v2 – v1
2
2
2
Multiply both sides by m
W = mad = m(v2 – v1)
2
2
2
W = mv2 – mv1
2
2
2
2
mv2 – mv1
W=
2
2
2
2
Work is the change in Kinetic Energy
mv
KE =
2
2
W = DKE = KE2-KE1
mv
KE =
2
2
W = DKE = KE2-KE1
Work done on an object is equal to its change in KE
Either to speed it up or slow it down.
(disclaimer --if no friction or PE stored)
What is the change in kinetic energy for a 5
kg car which speeds up from 10 m/s to 20
m/s?
How much work was done on the car?
Change in Kinetic Energy from 0 to 1 m/s
and from 1 to 2 m/s
90
Kinetic Energy
80
70
60
50
40
30
20
10
0
0
1
2
Velocity
3
4
5
Will the work be positive or negative?
Will the cars KE increase or decrease?
Force
Displacement
POSITIVE WORK Increases an objects KE
Will the work be positive or negative?
Will the cars KE increase or decrease?
Force
Displacement
Negative WORK Decreases an objects KE
A 100 N force is applied over 5 m to a:
1 kg car at rest
&
2 kg car at rest
Afterwards which car has more KE
Afterwards which car is moving faster?
An object is initially at rest. If a 250 N force
propels it forward and a 110 N force pushes it
backward, how much kinetic energy does the
object possesses after moving forward for
10.0 m?
A car has 450 J of kinetic energy. How far
would the car continue to travel if a force
of 310 N was applied opposing its motion?
If the object is has twice as much KE,
Twice as much work must be done to stop it.
So the car with twice as much KE
skids for twice as long
(if equal braking force)
1 kg
1m
2 kg
2m
Compare the stopping distances for cars of
equal mass, but different speeds
(hint: think KE)
10 m/s
1m
20 m/s
4m
40 m/s
16 m
What is the kinetic energy of a person
who is sitting at their desk?
They are stationary compared to the floor.
Are they stationary?
Velocity is relative and so is Kinetic Energy,
you can not really say how much energy an
object has because it is not really something
an object “has”. It is a comparison
Potential Energy:
Energy an object has “stored” due
to position
Because a position is relative
( or compared to something else)
Potential Energy is always a comparison
(not absolute measurement)
Potential Energy
UG = m g h
mass
(kg)
This compares the PE
to another height really
height
(m)
9.8 m/s2
Potential Energy-- is a comparison between 2 positions
-- there must be a force on the object
The boulder has
potential energy
due to gravity
HOW much PE does the boulder have?
A 2.0 kg rock is lifted 3.0 m.
How much work was done on it?
What is its potential energy?
2kg
3m
Work = Fd
Fg = mg = 2 kg * 9.8 m/s2 = 19.6 N
Work = m g d = 19.6 N 3.0 m = 59 J
Its potential energy increased because work was done on it
Gravitation PE does not depend on the path!!!!
m
m
m
PE = mgh
h
Just mass, height, and gravity
Work = DPE
m
m
m
The work done on each rock is the
same as the left one. (if no friction)
How can this be?
Elastic Potential Energy
Many materials will resist changing shape (deforming)
Archery bow, spring, rubber band
To change them from there “natural” state you
must apply a force over a distance.
In other words you do work on them.
Natural State
Stretched
d
If deformed a little objects will store that
energy as PE.
BUT…If you go beyond the ELASTIC LIMIT
Rubber breaks
Springs Stretch
Archery bows snap
Most objects (within their elastic limit) act
like springs and obey Hooke’s Law:
Fs = - k x
Force exerted by
the “spring” (N)
Spring Constant
How “stiff” the
spring is (N/m)
WHY THE NEGATIVE
How far the
spring is stretched
from it “natural”
position (m)
y
x
Direction
Displacement
spring will pull
(+ or -)
Force
(+ or -)
Stretched
+
-
Natural
State
0
0
-
+
Compressed
Fs = - k x
A spring will always exert a force in
the direction opposite the way is was
moved from the natural state
Natural
State
Fs = 0
x
Fs
Stretched
x
Fs
Stretched
further
Fs = - k x
The further the spring is stretched the
harder it will pull back!!!!
The negative means the spring is
pulling the opposite of the way it is
stretched
A spring is naturally .50 m long, when
stretched to .80 m what force will the
spring exert (on whatever is holding) if
the spring constant if 2.6 N/m
Work = F*d
average
kx
Force
(N)
The AREA under
the curve W= F*d
00
Distance (m)
x
The work done to compress or stretch a spring is
W=Fd
average F = kx
2
W = kx d =
2
kx x
2
x is also the distance
the force was exerted
2
kx
= 2
Since the work done on a spring is
2
kx
WS = 2
This is also how much energy was put into it SO
US =
kx2
2
x
Work = F*d  0 Fdx  0 kxdx
x
kx
Force
(N)
The AREA under
the curve W= F*d
00
Distance (m)
x
The FORCE on a spring goes up with a
linearly when it is stretched. This is why the
scale on a spring scale is not logarithmic.
The Energy required to stretch a spring is
exponential, because the force increases as it
is stretched or compressed.
When a spring is stretched 0.30 m from its
natural state it takes a force of 18 N to keep
it there.
What is its spring constant?
How much PE does it have?
What if it was stretched twice as far?
How much PE does a 150 kg rock gain if it moves up 2 meters on
a planet with no gravity?
m
How much force was exerted? NONE
How much work was done?
NONE
How much energy did it gain?
NONE
If gravity were “turned off” this rock would
have NO potential energy due to its height!!
An object only gains PE if:
1.) work was done against a force
&
2.) if that energy stored in a way that
it can be used
Which has more potential energy a
100 kg mass which is lifted up 5
meters above the ground on earth or
the moon.
Earth
Moon
Same
How much work is done to push a 35 kg object
up the frictionless ramp below (on earth)?
35 kg
25 m
33o
35 kg
Two magnets repel each other how would
you increase their potential energy?
What if one is switched so that they
both attract?
Some times when energy is added to a
substance it gets hotter (temperature goes up)
What type of energy does Temperature
indicate (KE or PE)
Atoms at different temperatures applet
KE & PE LAB
POWER
The rate at which work can be done
What does rate mean here?
Work
POWER =
Time
Which is more powerful a motor which can do:
100 J of work in 2 seconds
or
100 J of work in 1 seconds
Work (J)
POWER =
Time (s)
POWER has units of J/s
Also called a watt (W)
Or
kg m2 If you prefer
s3
1 Watt =
1J
1s
1,000 J
1 kW = 1000 W =
1s
An electric device like a heater or light
bulb is rated in watts.
This tells you the rate at which it uses electrical
energy to do work.
Running up a set of stairs
Walking up a set of stairs
Both do the same work
BUT one needs more power!!!
Both motors do the same amount
of work but one can do it faster
because it has more power
1 kg
1 kg
What about here?
What’s the same & different?
1 kg
10 kg
What about here?
1 kg
1 kg
A 35 kg box is lifted from the floor to a height
of 2.3 m in 3.0 seconds by a forklift. What is
the power of the forklift?
One that is twice as powerful would have done
it in….
Half as powerful…
What power would be required to
accelerate a 2700 kg car from 0 to 15 m/s
in 10 seconds?
If a motor rated for 60 W were to lift a 50 kg
student vertically. What would there
upward velocity be?
POWER
In the SI system, power is rated in Watts or KW
The power of your car is rated in:
Hp (horsepower)
1 hp = 746 W
The mazda RX-8 has the following
specifications. 232 HP
1360 Kg
How long would it take to reach a
speed of 27 m/s (60 mph) from rest
What is its theoretical acceleration?
How many g’s?
work done here is changing KE
W
P=
t
SKIP
W = DK = K2-K1
K=
mv 2
2
0
Power Lab
ENERGY is conserved
What does it mean in science when
something is conserved?
Uh Like,
quit wasting
electricity
NO
Energy is conserved means:
Initial Energy = Final Energy
Energy is conserved means:
Energy doesn’t get “produced” or
destroyed it just changes forms
between types PE & KE
(often moving from 1 object to another)
Force x distance
Work
moves energy around
&
changes energy from 1 type to
another
Energy is like money
Work is like spending it
J
J
J
J
Gravity
doesitwork
on
Just before
hits the
the
massitand
changes
ground
is all
in the
the
form
of the
form
of kinetic
energy
energy
Gravitational
PE
Heat
Kinetic
Energy
When it hits the
ground,
the mass does work
on the ground
Gravitational
PE
Heat
Kinetic
Energy
Even though the
energy changes we
always have the same
amount
Gravitational
PE
Heat
Kinetic
Energy
Conversion of energy in happy / sad balls
Where does the energy go?
Energy changing form
Total Energy is Conserved
Energy changes in a pendulum
For a swinging Pendulum
start
h
100 J PE
h
75 J KE
25 J PE
100 J
KE
KE
The total energy at any time is the same
(if no friction)
100 J PE
Which ball will have the faster velocity when it reaches the bottom?
If there is no friction
The same!!!
What if the red ball was twice as heavy?
Still the same!!!
Each Rock has the same Initial PE
m
m
m
So each rock would have the same KE
when it reached the bottom.
THE TOTAL ENERGY IS CONSTANT
THE TOTAL ENERGY IS CONSTANT
PE
PE
KE
PE
PE
KE
KE
KE
KE
Where will the car be moving the slowest?
PE
KE
PE
KE
Where will the car be moving the FASTEST?
PE
KE
KE
At what spots on the ride will the car
have the same speed as it does now?
Anytime it is at the same height?
PE
KE
Why might this rollercoaster designer be fired?
Let’s go
Uh oh
PE
PE
KE
KE
The total energy of a system doesn’t change
(if there is no friction, this is a non-conservative force)
Total Energy(initial) = Total Energy(Final)
U 1 + K 1 = U2 + K 2
Gravitational and Elastic are the big ones
A pendulum (with a mass of m kg) is attached to a 25
cm string. If released from rest how fast is it traveling
at the bottom of its swing in the picture below?
.11 m
Compare the speeds of the two
rocks when they reach the
bottom of a frictionless ramp?
5.0 m
6.0 m
5.0 m
10.0 m
A 150 kg rollercoaster car.
A
20 m
C
15 m
15 m
B
0m
If the car started at from rest at the top how
fast is it moving at points A, B, and C?
Does the answer depend on the mass?
A cannon ball is fired from a cliff at 35
m/s at 60o above the horizontal. If the
cliff is 130 m tall, how fast is it going
when it hits the ground below?
A 5 kg rock is compressed into a spring such that the spring is .25
meters shorter than its natural state.
The spring constant is k = 1,500 N/m
How fast is the rock moving when it just leaves the spring.
How high does it go compared to its original height?
5kg
? m/s
5kg
0.25 m
?m
5kg
initial
State 2
State 3
Back to our bungee jumper (mass of 75 kg), if he falls 15 m
before the cord starts to stretch, how high does the bridge need
to be if the spring constant of the cord is 50 N/m?
15 m
15 m
?m
ym
Quadratic solver
Conservation of Energy Lab
Energy is conserved if there is no friction.
Does friction destroy energy?
FRICTION
Energy
The forces we have looked at currently are called
CONSERVATIVE FORCES.
Like gravity, a push, springs, etc...
Because the work that they do is conserved in the
system.
Friction is a non-conservative force because the work
allows energy to leave the system.
No
Friction converts PE & KE
into heat.
The total amount of energy is the same
PE1 + KE1 = PE2 + KE2 + Energy Lost
Friction does not destroy the energy, it just
converts it to heat so will not go as high
PE
PE
PE
KE
KE
Energy
converted to
heat in red
PE
KE
KE
This energy is no
longer available to
help the car go up the
hill.
Because of friction the hills must be lower as the
ride goes on. (unless energy is added)
Let’s go
If the rollercoaster gets hot due to friction,
that energy won’t stay in the rollercoaster.
It will warm up surrounding objects.
Total Energy in the Universe is always CONSERVED
Universe (initial)
Universe (Final)
=
No energy is lost, where would it go?
The total “units” of energy is constant but
it changes form and location
When we make measurements we have
to define a system, because we can’t
measure the whole universe!!!
A “system” just includes objects of interest.
Such as:
a rollercoaster
a ball dropping
a box sliding
Universe -initial
(6 units)
Universe -Final
(6 units)
the system
(3 units)
the system
The total energy of the universe is constant
But your “system” can lose or gain energy to the
universe
Work done against
FRICTION IS “LOST”
(from the system).
WFRICTION = FFd = ELOST
A 2.4 kg ball starts from rest and rolls down the ramp below. Its velocity
at the bottom of the ramp is 11 m/s.
---What is the system?
---Did the system lose energy?
12 m
19 m
A 2.4 kg crate starts from rest and is pushed up the ramp a distance of
22.5 m with a force of 15.0 N and comes to a stop at the top.
12 m
---What is the system?
---How much work was done?
---How much energy did the crate gain?
---How much energy was lost?
--- What was the FF
22.5 m
19 m
A 2.4 kg crate starts from rest and is pushed at a constant velocity along
the ground a distance of 19 m with a force of 15.0 N. After 19 m the
crate immediately stops.
---What is the system?
---How much work was done?
---How much KE & PE did the crate gain?
---How much energy was lost?
--- What was the FF
15.0 N
19 m