What is work?
Explanation Videos:
Physics Definition of Work with
practice problems
Based on the video of work,
Which people are doing work and why?
a light
2. Lifting
cardboard box
1.
F
F
4.
Walking with
drinks at a
constant speed
F
F
Mowing the lawn
Holding a large
stack of books
at rest
F
6.
5.
F
3.
Pushing a crate
at a constant
speed across the
floor
7.
A satellite
orbiting Earth
Lifting Weights
Work?
1
No, no displacement
2
Yes, work against gravity (W=Fgd)
3
No, force and displacement are not in the same direction (they are perpendicular)
4
Yes. (W=Fdcosθ)
5
Yes (W=Ffd)
6
Yes (W=Fgd)
7
No, the force and displacement are not in the same direction (they are perpendicular)
What is the physical definition of work
and how do we calculate it?
• Work occurs when a force applied to an object
causes that object moves through a displacement.
– The direction of the displacement must be in the same
direction as the force (or component of the force) doing
the work!
– Formula:
W=Fd
(work = force x displacement)
• Work is a scalar quantity (has NO direction, ie North or South)
• But work can be positive or negative (Lost or gained)
• Force and displacement are both vectors (you can only
multiply numbers that are in the EXACT SAME DIRECTION!)
– Units: J=Nm (Joule = Newton x meter)
W=Fd
Work done against gravity
• The man lifts a 5Kg box initially on the
ground at a constant speed to a height 1.4m
above the ground.
– Draw a free body diagram of the forces acting on
the box. (make sure the length of the arrows
represent the relative strengths of the forces)
– How much force is the man putting on the box?
– How much work is done by the man while lifting
the box?
W=Fgd=mgd= 68.6J
W=Fd
Work done against gravity
• The women does 300J of work while lifting the
weights 0.75m in the air.
W=Fgd
– How much does the barbell weigh?
– What is the mass of the barbell?
300J = Fg (.75m)
Fg=400N
Fg=mg
400N = m (9.81m/s2)
m= 40.8kg
• The weights are then lowered back to their original
height, how much total work is done by the
of work because the total
women? Zero joules
displacement is zero
Positive vs. Negative Work
• When doing work against
gravity,
– lifting things into the air is
The force is in the same
direction as the displacement
and the energy of the object
increases.
• considered positive work by the
person doing the lifting.
• Negative work by gravity
– lowering things back to the
ground
The force is in the
opposite direction
of the displacement
The force is in the opposite
direction of the
displacement and the energy
of the object decreases
• considered negative work by the
The force is in the
person
same direction as
the displacement
• positive work by gravity
Work done against friction
horizontal force
W=Ff d
• The man pushes a 50Kg wooden crate box
at a constant speed across a wooden floor
covering a distance of 12m (coefficient of
friction is 0.3)
– How much force is the man applying on the
box to keep it moving at constant speed?
– How much work is done by the man while
pushing the box?
𝑊 = 𝐹𝑑
𝑊 = 147𝑁 12𝑚
𝑊 = 1766𝐽
𝐹𝑥 = 0
𝐹𝑎𝑝𝑝 − 𝐹𝑓 = 0
𝐹𝑎𝑝𝑝 = 𝜇𝐹𝑁
𝐹𝑎𝑝𝑝 = 0.3(50 × 9.81)
𝐹𝑎𝑝𝑝 = 147𝑁
Work done on an angle
angled force
W=Fdcosθ
• The child applies a 45N force at an angle of
50o to push a 3.5kg mower 20m across the
lawn at a constant speed.
𝐹 =𝐹
cos 𝜃
𝑥
𝑎𝑝𝑝
– How much force is the child putting on the
mower in the direction the mower is moving? 𝐹𝑥 = 45𝑁 cos 50
𝐹𝑥 = 29𝑁
– How much work is done by the child while
pushing the mower?
𝑊 = 𝐹𝑑
𝑊 = 29𝑁 20𝑚
𝑊 = 580𝐽
examples
1.
A 9kg box is lifted at a constant
speed to a height of 4m by a fork lift.
How much work does the fork lift
do?
2.
A weight lifter does 400J of work
when lifting his weight a distance of
1.2 meters above the ground. What
is the mass of the weight he is
lifting?
3.
A mother applies a constant 67N
horizontal force while pushing a
shopping cart at a constant speed
down a 13m long aisle in the market.
How much work does the mother
do?
4.
If 320J of work are done while
pushing a 55Kg sofa 2.3m across the
floor at a constant speed, what is the
coefficient of kinetic friction between
the sofa and the floor?
𝑊 = 𝐹𝑑
𝑊 = (9)(9.81) 4
𝑊 = 353𝐽
𝑊 = 𝐹𝑑
400= (𝑚)(9.81) 1.2
𝑚 = 34𝑘𝑔
𝑊 = 𝐹𝑑
W= (67) 13
𝑚 = 871𝐾𝑔
𝑊 = 𝐹𝑓 𝑑
320J=μ(55)(9.81) 2.3
μ =0.26
Do Work Mastering Physics Now
Power
“the rate at which
work is done”
Power Explanation video
Aim: What is mechanical power and
how do we calculate it?
• Mechanical Power is defined as the amount of
work done per time.
W
• Formula: P 
t
• P is the symbol for power in an equation
• The unit of power is the Watt (W)
• A Watt is equal to a Joule/second (J/s)
Examples
1. A man brings a 7Kg box up the stairs to the
second floor of his house that is 10m above the
ground. If it takes him 20 seconds to get up the
stairs,
a. How much work does he do?
b. What is the power he develops?
𝑊 = 𝐹𝑔 𝑑
𝑊 = 7 9.81 10
𝑊 = 687𝐽
𝑊
𝑃=
𝑡
687
𝑃=
20
𝑃 = 34𝑊𝑎𝑡𝑡𝑠
Examples
2. A fork lift generates 3000W of power
when lifting a car 3m in the air in 10
seconds.
a. How much work does the fork lift do?
b. What is the mass of the car?
3. A body builder generates 2000Watts
of power when lifting 150kg mass
0.9m in the air.
a. How much work does the body builder
do?
b. How much time does it take the body
builder take the lift the masses up?
𝑊
𝑃=
𝑡
𝑊
3000 =
10
𝑊 = 30000𝐽
𝑊 = 𝐹𝑔 𝑑
30000= 𝑚 9.81 3
𝑚 = 1019𝑘𝑔
𝑊 = 𝐹𝑔 𝑑
W= (150) 9.81 0.9
𝑊 = 1324𝐽
𝑊
𝑃=
𝑡
1324
2000 =
𝑡
𝑊 = 0.66𝑠
Power On an angle
angled force
𝐹𝑥 = 𝐹𝑎𝑝𝑝 cos 𝜃
𝐹𝑥 = 60𝑁 cos 55
𝐹𝑥 = 34𝑁
4.
The child applies a 60N force at an angle of
55o to push a 3.5kg mower 20m across the
lawn at a constant speed in 30 seconds.
– How much force is the child putting on the
mower in the direction the mower is moving?
– How much work is done by the child while
pushing the mower?
– What is the power generated by the child?
𝑊 = 𝐹𝑑
𝑊 = 34𝑁 20𝑚
𝑊 = 688𝐽
𝑊
𝑃=
𝑡
688
𝑃=
30
𝑃 = 23𝑊𝑎𝑡𝑡𝑠
A second way to calculate Power
W
P
t
Fd
P
t
d 
P  F 
t
P  Fv
Examples
5. An engine provides a 3000N
force to keep a car moving at
a constant speed of 25m/s.
What is the power of the
engine?
6. A remote controlled car has
an engine that can provide
18W of power to cause a car
to move at 3m/s. What is the
force provided by the car’s
engine?
7. An elevator motor provides
10KW of power while lifting a
450Kg elevator at a constant
speed. What is the speed of
the elevator?
𝑃 = 𝐹𝑣
𝑃 = 3000 (35)
𝑃 = 75000𝑊𝑎𝑡𝑡𝑠
𝑃 = 𝐹𝑣
18= 𝐹 (3)
𝐹 = 6𝑁
𝑃 = 𝐹𝑣
10,000 = 450 (9.81)(𝑣)
𝑣 = 2.3𝑚/𝑠
Work Graphically
To calculate the
work done, find
the area under the
curve
F(N)
10
d(m)
𝑊 = 𝑎𝑟𝑒𝑎
𝑊 = 10 6
𝑊 = 60𝐽
6
15
F(N)
𝑊 = 𝑎𝑟𝑒𝑎
𝑊 = .5 10 15
𝑊 = 75𝐽
d(m)
10
Do Power Mastering Physics Now
Potential
Energy Due
to Gravity
Think about it:
Describe what you would
feel if you were the guy in
the picture to the left.
DO NOW:
What does it mean to say
“you have a lot of
potential” to someone?
Aim: What is potential energy?
• The word potential in general means the
ability to do something.
– Athletic Potential: you have the ability to perform
well at athletics
– Academic Potential: you have the ability to do
well academically.
• Gravitational Potential Energy: An object has
the ability to do work based on its position
above the ‘ground’
Gravitational Potential
Energy
• An object has the ability to do work because of its
gravitational position
• The gravitational potential energy PEg of an object
depends on
– Its mass m measured in Kilograms
– Its height above the chosen reference point h measured in
meters
– The gravitational acceleration on the planet g (9.81m/s2 on
Earth).
PEg  mgh
PEg  mgh
10Kg
• Calculate the gravitational potential
energy of the following objects
8m
20Kg
3m
𝑃𝐸𝑔 = 𝑚𝑔ℎ
𝑃𝐸𝑔 = 15 (9.81)(−2)
𝑃𝐸𝑔 = −294𝐽
𝑃𝐸𝑔 = 𝑚𝑔ℎ
2m
𝑃𝐸𝑔 = 20 (9.81)(3)
𝑃𝐸𝑔 = 589𝐽
𝑃𝐸𝑔 = 𝑚𝑔ℎ
𝑃𝐸𝑔 = 8 (9.81)(−1.5)
𝑃𝐸𝑔 = 589𝐽
Reference Point
0.0m
1.5m
8Kg
15Kg
𝑃𝐸𝑔 = 𝑚𝑔ℎ
𝑃𝐸𝑔 = 10 (9.81)(8)
𝑃𝐸𝑔 = 785𝐽
Kinetic Energy
𝑊 = 𝐹𝑑
𝑊 800 4.5
𝑊 = 3600𝐽
Do Now:
A horizontal force of
800N is applied to a
bobsled over a
distance of 4.5m.
How much work is
done on the
bobsled?
Kinetic Energy Defined
• Kinetic energy is the energy a moving object has.
• The kinetic energy KE of an object depends on
– The mass m of the object in Kilograms
– The velocity v of the object in m/s
• Formula KE  1 mv 2
2
2
Kgm
• Units: Joule 
s2
• Kinetic energy can never be a negative value
– Mass is always positive
– Velocity can be negative, but when squared, it becomes
positive
1 2
KE  mv
2
1. A 1200Kg car is moving down
𝐾𝐸 = 1 2 𝑚𝑣 2
the road at 14m/s. What is
𝐾𝐸 = 1 2 (1200)(142 )
the kinetic energy of the car?
𝐾𝐸 = 117600𝐽
2. A 30g bullet has a kinetic
energy of 30,000J. What is the
speed of the bullet?
3. An object has 500J of Kinetic
energy when moving at 6m/s.
What is the mass of the
object?
𝐾𝐸 = 1 2 𝑚𝑣 2
30000 = 1 2 (.03)(𝑣 2 )
𝑣 = 1414𝑚/𝑠
𝐾𝐸 = 1 2 𝑚𝑣 2
500 = 1 2 (𝑚)(62 )
𝑚 = 27.8𝑘𝑔
Do Conservation of Energy Mastering
Physics Now
Potential Energy due to Gravity
Elastic Force and
Hooke’s Law
The Elastic Force
• The elastic force is a “restoring
force” because it always pulls
back towards its original
starting position.
– Think of a spring for example.
Every spring has a natural rest
length
– If stretched to the right, the
spring will pull to the left.
– If compressed to the left, the
spring will push back towards
Fapplied
the right.
The spring is always trying to
restore its original length
Fspring
Fspring
Fapplied
Hooke’s Law
Fs = kx
• There is a linear relationship between
the force applied to a spring (Fs) and the
resulting change in length of that spring
(x) if the elastic limit has not been
reached
• k is known as the spring
constant and describes
Fs
how easily a spring can
be stretched. k has the
units of N/m
Fapp
x
Objects that Follow Hooke’s Law
Stiffer spring
(higher slope =higher k)
Fs
Object that follow
Hooke’s Law have
linear graphs when
the force applied to
Looser Spring
(Lower slope = lower k) them is graphed
versus the change
in length of that
object. The slope
of the graph is the
x
spring constant
Things to watch out for!
• Make sure the force (F) is in Newtons and the
change in length (x) is in meters!
• Make sure you are using a change in length of the
spring, not the actual length of the spring!
• On a graph, the slope of a F vs. x graph will be k
• The slope of a x vs. F graph will be 1/k
Practice Questions
1.
A spring can be stretch 0.3m from
its original length by applying a
force of 10N. What is the spring
constant for that spring?
2.
The same spring is now
compressed 0.15m. What force
would it take to achieve this
compression?
𝐹𝑠 = 𝑘𝑥
𝐹𝑠 = (33.3) 0.15
𝐹𝑠 = 5𝑁
3.
A spring has a spring constant of
90N/m. If this spring is originally
10cm long and is compressed to
5cm, what force was applied to the
spring?
𝐹𝑠 = 𝑘𝑥
𝐹𝑠 = (90) 0.05
𝐹𝑠 = 4.5𝑁
4.
A spring has a constant of 100N/m.
What is the change in length of
that spring when a 55N force is
applied?
𝐹𝑠 = 𝑘𝑥
55 = (100) 𝑥
𝑥 = 0.55𝑚
𝐹𝑠 = 𝑘𝑥
10 = 𝑘 0.3
𝑘 = 33.3𝑁/𝑚
Elastic Potential
Energy
What is PEs?
How do we calculate PEs?
How do we used PEs in our
lives?
Elastic Potential Energy
• Elastic potential energy is the energy stored in a
stretched or compressed elastic object.
– It depends on the…
• k (the spring constant in N/m)
• x (the amount that object has been compressed or stretched)
– Formula
• PEs=1/2 kx2 units: Joules
Fs
x
1.
Example Questions
Fs=kx
PEs=1/2kx2
A spring with a spring constant of
135N/m is compressed 0.2m
a.
b.
2.
𝐹𝑠 = 𝑘𝑥
𝐹𝑠 = (135) 0.2
𝐹𝑠 = 27𝑁
What is the force that caused this
compression?
What is the energy stored in the spring?
A 240N force causes a spring to compress
0.25m.
a.
b.
What is the spring constant of that
spring?
How much energy is stored in that
spring?
𝑃𝐸𝑠 = 1 2 𝑘𝑥 2
𝑃𝐸𝑠 = 1 2 (135)(0.22 )
𝑃𝐸𝑠 = 2.7𝐽
𝐹𝑠 = 𝑘𝑥
240 = (𝑘) 0.25
𝑘 = 960𝑁/𝑚
𝑃𝐸𝑠 = 1 2 𝑘𝑥 2
𝑃𝐸𝑠 = 1 2 (960)(0.252 )
𝑃𝐸𝑠 = 30𝐽
Do Energy Mastering Physics Now
Work Energy Theorem
• Watch the above video for good practice
problems and examples of the work energy
theorem.
Work as a change in PEg
Work done by Friction / Internal
Energy
• Internal energy (symbol U) is the equal to the work
done by friction in a system.
• It is also called heat.
• Is can be calculated by
– finding the difference between the actual work done
(W=Fd) and the resulting energy of the object (kinetic if
moving, potential if above the ground)
– Calculating the energy lost during motion
• U = E final- E initial
Example 1:
For a 1.2kg cart dragged to a height
of 0.9m up a distance of 1.7m by a
force of 15N.
-
𝑃𝐸𝑔 = 𝑚𝑔ℎ
𝑃𝐸𝑔 =(1.2)(9.81)(0.9)
What is the gravitational potential of the cart
𝑃𝐸𝑔 = 10.6𝐽
at the top?
-
What is the work done on the cart?
-
What is the work done against friction?
𝑊 = 𝐹𝑑
𝑊 = (15) 1.7
𝑊 = 25.5J
𝑊 = ∆𝐸 + 𝑈
25.5 = 10.6 + 𝑈
𝑈 = 14.9𝐽
Example 2:
A women does 300J of work lifting a 2kg block
10m in the air using a rusty pulley system.
How much work was done against friction?
𝑃𝐸𝑔 = 𝑚𝑔ℎ
𝑃𝐸𝑔 =(2)(9.81)(10)
𝑃𝐸𝑔 = 196𝐽
𝑊 = ∆𝐸 + 𝑈
300 = 196 + 𝑈
𝑈 = 104𝐽
Work as a change in
Kinetic energy
• When pushing an object, the work you do is
equal to the object’s change in kinetic energy
(when friction is NOT present)
• W=ΔKE
• A horizontal force of 800N is applied to a
250Kg bobsled over a distance of 4.5m.
– How much work is done on the bobsled?
– How fast is the bobsled going after the they are
done pushing?
1. In a drag race, a 120Kg car reaches a speed of
30m/s over a distance of 20m. (neglecting friction)
-
What is the car’s change in kinetic energy?
How much work is one by the car’s engine?
What force does the engine put on the car?
2. A 60kg runner runs a 5k in 25 minutes
-
What is the average velocity of the runner?
What is the kinetic energy of the runner?
3. A women pushes her 20Kg son on a swing. She
applies a 50N force over a distance of 0.75m
- What is the velocity of the kid after being pushed
assuming there is no friction?
Work as a change in
Kinetic energy
(with Friction)
• When pushing an object, the work you do is
equal to the object’s change in kinetic energy
PLUS the work done against friction
• W=ΔKE+Wf
• A horizontal force of 300N applied for a
distance of 20m causes a 20Kg crate to reach a
speed of 23m/s. How much work was done
against friction?
Conservation of Mechanical Energy
• WITHOUT friction, the total mechanical energy of a
system is conserved
– Remember, total mechanical energy (ET) is the sum of
• PEg=mgh
• KE=1/2mv2
• PEs=1/2kx2
– When solving conservation of energy questions, you
need to ask yourself if the object possess each type of
energy at the point of interest.
– To find the total mechanical energy (ET) at a point, add
up the energies it has.
– This total will NEVER CHANGE!
Do Conservation of Energy Mastering
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Review of gravitational potential energy and
kinetic energy
Type of
At rest at the top energy it has
Energy
Transfers
Type of
energy it has
Bungee is back to rest length
Starting to fall
On the way back up
Bungee starts to stretch
Back to original position
Bungee at max length
Energy
Transfers
Type of
At rest at the top energy it has
Energy
Transfers
PEg + KE
PEg +
max KE
PEg is decreasing
and transferring to
KE
KE is transferring
to PEg
PEg and KE are
decreasing and
transferring to PEs
Back to original position
All PEg
Bungee at max length
PEs max
PEs transferring
back into max KE
and PEg
On the way back up
Bungee starts to stretch
PEg +
max KE
Energy
Transfers
Bungee is back to rest length
All PEg
Starting to fall
Type of
energy it has
PEg and KE are
zero and
transferred all to
PEs
Victoria Falls: 111m high
1. What is her total energy in
situation 1?
2. What is her potential
energy in situation 3?
3. What is her kinetic energy
in situation 3?
4. How fast is she moving in
situation 3?
40m bungee
55kg person
5. What type of energy does she
have in situation 4?
6. How far did the bungee stretch
while in situation 4?
7. What is the spring constant of
the bungee cord?