Energy: ability to do work

1
Energyability to do work

• Another way of analyzing motion

2
Work

• In physics we say that work is done on an object
  if a force is applied to it and that force causes
  it to move a certain distance.

Work W Fd
N
m
WORK IS ENERGY!!!
Nm J Joule
3
What is a Joule?
N m
kg m m s2
kg m2 s2
The energy required to lift a small apple one
meter straight up.
4
Heres the important thing about workwork is
only done if the force has a component in the
same direction as the displacement.
m 10 kg
F 25N
d 2m
Is this guy doing work on the box?
Yes. The force vector is in the same direction
as the displacement.
How much work is being done?
W Fd
W 25N(2m)
W 50 Nm 50J
5
Is work done when pulling this dog?
Yes. The force vector has some component in the
same direction as the displacement.
How much work is being done?
F
Fy
30
Fx
Fx cosT A H
70N
Fx FcosT
30
Fx 70Ncos30
d 10m
Fx 61N
W Fd
W 61N(10m)
W 610J
6
Is work being done by this waiter?
No. He could carry around that tray all day and
according to physics he wouldnt be doing any
work. There is a force (the waiter pushes up on
the tray) and there is a displacement (the tray
is moved horizontally across the room). Yet the
force does not cause the displacement. To cause
a displacement, there must be a component of
force in the direction of the displacement.
7

• How much work is needed to lift at a constant
  speed a 15kg book 3m?

W Fd
W mgd
W (15kg)(10m/s2)(3m)
W 450 J
8
Which path (incline vs. ladder) requires more
work to get the box to the top?
mbox 10 kg
10 m
5 m
30
W Fd
W Fd
W (50N)(10m)
W (100N)(5m)
W 500 J
W 500 J
Same amount of work!
9
A particular task may require a certain amount of
work but it might be done over different lengths
of time

• This is known as Power (P). It measures the rate
  at which work is done.

P W t
d v t
P Fd t
P Fv
J watt W s
P Fd t
10
Who has more power?

• Dan Parker and Brad Bowen are in the
  weightlifting room. Dan lifts the 50 kg barbell
  over his head 10 times in one minute Brad lifts
  the 50 kg barbell over his head 10 times in 10
  seconds. Which student does the most work?
  Which student delivers the most power?

Brad is more "power-full" since he does the same
work in less time. Power and time are inversely
proportional.
11
Try this

• A crane lifts a load with a mass of 1000kg a
  vertical distance of 25m in 9s at a constant
  velocity. How powerful is the crane?

P W Fd t t
Fgd t
mgh t
(1000kg)(10m/s2)(25m) 9s
27000 W
12
Try this

• A 45 kg bicyclist climbs a hill at a constant
  speed of 3 m/s by applying an average force of 80
  N. How much power does the bicyclist develop?

P Fv
P (80 N)(3 m/s)
P 240 W
13

• Power is a rate (ENERGY PER SECOND).
• Your electric bill (power bill) is based on your
  rate of energy use.
• A lightbulb with a 60 Watt power rating means
  that the bulb uses 60 joules of energy per second.

W ?ET
Work a change in total energy
14
Energy is the ability to do work!

• Energy is measured by the amount of work it can
  do.

15
Energy comes in different forms

• Potential energy (PE)
• Energy possessed by an object due to its position
• Sometimes referred to as stored energy

16
Gravitational Potential Energy

• If an object, originally at rest on Earths
  surface, is lifted to some height, work is done
  against the gravitational force.
• The work done in lifting the object is equal to
  the objects gravitational potential energy.

17
work done gravitational potential energy
W ?PE
W Fd
Fg
w
mg
W mgd
h
?PE mgh
18
Knowing that the potential energy at the top of
the tall platform is 50 J, what is the potential
energy at the other positions shown on the stair
steps and the incline?
19
Path doesnt matter
Remember that the changes in an object's
potential energy only depend on comparing its
starting position and its ending position, not
on whether it does or does not pass through
various points in-between.
20
Try this

• How much potential energy is gained by an object
  with a mass of 2 kg that is lifted from the floor
  to the top of a .8 m high table?

?PE mgh
?PE (2kg)(10m/s2)(.8m)
?PE 16 J
21
Try this

• King Kong is on top of the Empire State Building
  426 m above the surface of the Earth. What is
  his gravitational potential energy relative to
  the ground? Lets say his mass is 1000 kg (a
  metric ton).

?PE mgh
?PE (1000kg)(10m/s2)(426m)
?PE 4,260,000 J
22
Draw how the graph would look that represents
this relationship- PE vs. h
?PE mgh
PE mg h
PE
What if m .1 kg
h
23
Elastic Potential Energy

• Energy can be stored in a spring and is measured
  as the work required to stretch or compress it.

24
Remember Hookes Law

• The compression or elongation of a spring is
  directly proportional to the applied force.

Fs kx
Spring constant
The larger the k, the stiffer the spring.
25
x
F
Whats the spring constant of this spring?
F kx
k F x
25 N .50 m
50 N/m
26
Potential Energy of a Spring
W PEs
W Fd
x
½ kx
PEs ½ kx2
27
What would the graph look like that shows this
relationship- PE vs. x?
PE
PE
PE
PE
x
x
x
x
PEs ½ kx2
What if we made k 2 N/m
PEs x2
28
Elastic potential energy can be stored in rubber
bands, bungee chords, trampolines, springs, an
arrow drawn into a bow, etc.
29
Try this

• A force of 50 N is needed to compress a spring a
  distance of 1 m. What is the potential energy
  stored in the compressed spring?

PEs ½ kx2
Fs kx
k 50 N 1 m
PEs ½ (50)(1m)2
Fs kx x x
PEs 25 J
k 50 N/m
k Fs x
30
Try this

• When a spring is stretched .2 m from its
  equilibrium position, it possesses a potential
  energy of 10 J. What is the spring constant for
  the spring?

PEs ½ kx2
k 2PE x2
k 500 N/m
31
Kinetic Energy

• When a moving object strikes another object and
  displaces it, the moving object exerts a force on
  the second object and does work on it.

32
Kinetic Energy- the energy an object possesses
due to its motion.
W ?KE
W Fd
vt
from rest- v 2
ma
v t
W ?KE m v v t t 2
?KE ½ mv2
33
Try this

• What is the kinetic energy of a 980 kg race car
  traveling at 90 m/s?

?KE ½ mv2
?KE ½ (980kg)(90m/s)2
?KE 3,969,000 J
34
Try this

• Determine the kinetic energy of a 625-kg roller
  coaster car that is moving with a speed of 18.3
  m/s.

?KE ½ mv2
?KE ½ (625kg)(18.3m/s)2
?KE 104,653 J
35
Try this

• A platform diver for the Circus has a kinetic
  energy of 12 000 J just prior to hitting the
  bucket of water . If the divers mass is 40 kg,
  then what is her speed?

?KE ½ mv2
v2 2KE m
v 25 m/s
36
Conservation of Energy

• Energy can neither be created nor destroyed. But
  it can be transferred from one type to another
  (i.e. potential to kinetic) in a closed system.

37
Examples
The ball is losing height (falling h is
decreasing) and gaining speed (v is
increasing). Energy is transformed from PE
(height) to KE (speed).
Motion - A ball falls from a height of 2 meters
in the absence of air resistance.
38
Examples
The skier is losing height (the final location
is lower than the starting location) and
gaining speed (the skier is faster at B than at
A). Energy is transformed from PE (height) to
KE (speed).
Motion - A skier glides from location A to
location B across a friction free ice.
39
Examples
The ball is gaining height (rising) and losing
speed (slowing down). Energy is transformed
from KE (speed) to PE (height).
Motion - A baseball is traveling upward toward a
man in the bleachers.
40
Examples
The jumper is losing speed (slowing down) and
the bungee cord is stretching. Energy is
transformed from KE (speed) to PE (a stretched
"spring").
Motion - A bungee cord begins to exert an upward
force upon a falling bungee jumper.
41
Examples
The spring changes from a compressed state to a
relaxed state and the dart starts moving.
Energy is transformed from PEs (a compressed
spring) to KE (speed).
Motion - The spring of a dart gun exerts a force
on a dart as it is launched from an initial
rest position.
42
Closed System?

• A closed system is one in which there are no
  external forces doing work on the system, and no
  transfer of energy into or out of the system.
• External Forces- FA, Ff, FT, Fair, FN
• The total energy (ET) of a closed system ALWAYS
  remains the same.

43
Total Mechanical Energy

• In a closed (ideal) system

?PE ?KE TME
and
?PE ?KE 0
?KE - ?PE
44

• In a non-ideal system there is an external force
  acting on the system and the total energy is

internal energy- influenced by heat
ET PE KE Q
Heres the equation were going to use
W ?PE ?KE Wf
45
There are 3 different approaches we can take to
solve this problem
v 0
10 kg
A
1.
PE KE
mgh 1mv2 2
2mgh 1mv22 2
20 m
2mgh mv2 m m
v2 2gh
B
v2 2(10m/s2)(20m)
v ?
v2 400 m/s
20 m/s
46
0
0
2.
v 0
10 kg
A
W ?KE ?PE Wf
Any work being done on the system (W Fd)? Is
anyone pulling or pushing on the block?
Any friction?
No neglecting air friction
No
0 ?KE ?PE
20 m
0
0
0 KEf KEi PEf PEi
0 KEf PEi
KEf PEi
B
v ?
47
v 0
3.
10 kg
A

KE
PE
PEs
Wf
v
TE
A
B
0
½ mv2 2000 J
0
mgh 2000 J
20 m
0
0
0
0
0
v2 2gh 20 m/s
2000 J
2000 J
B
v ?
48
How could we of figured this out without energy?
v 0
10 kg
vi 0 m/s
a 10 m/s2
d 20 m
20 m
vf ?
vf2 vi2 2ad
vf2 2ad
vf2 2(10m/s2)(20m)
v ?
20 m/s
vf2 400 m/s
49

KE
PE
PEs
Wf
v
TE
A
C
B
KE TE PE 1320 J
½ mv2 1920 J
h ?
0
v 0 m/s
h PE/mg 3.2 m
0
mgh 600 J
0
0
0
C
0
0
0
v2 2gh 6.6 m/s
0 m/s
8 m/s
1920 J
1920 J
1920 J
B
A
Remember energy is another way of analyzing
motion.
50
(No Transcript)
51
(No Transcript)