Transcript 5-work

CP Physics Chapter 5
Work
and Energy
WORK (W)
Work is done when an applied force moves an object
F: force
d: displacement
: Angle between
F&d
W = F·d·cos
N·m
or
Joule (J)
d
Not a
vector!
usually
W = F·d
Wnet=Fnetd
As long as F and d are in the same
or opposite directions (parallel)
Example #1
A crate is pulled 5 m along a floor
by a 100 N horizontal force. What
is the work done by that applied
force?
Example #2
This time the crate gets pulled by
the 100 N force but at 25 angle
over the same 5 m distance.
What work is done by the
applied force this time?
Example #3
A student holds a 1.5 kg Physics book out the window
and stays perfectly still for 5 minutes. Finally her
arm is tired and she lets it drop (luckily it is caught
by a passing student).
a) How much work is done on the book by the
student while holding the book?
b) How much work is done by the force of gravity
if the book falls 3.0 m before being caught.
Example #4
0.15m
A student carries their 2.0 kg backpack (with Physics
book) from Physics to the stairway 30 m away.
The
student
then
goes
up
1
flight
of
stairs.
Each
0.15m
flight of stairs is made up of 20 stairs which are
each 0.15 m up and 0.15 m over (this means 3 m up
and 3 m horizontal). Their next class is 10m more.
a) How much work is done by the student on the
backpack while moving from class to the stairway?
b) How much work is done by the student on the
backpack while moving up the stairs?
Example #5
A 10 kg box is pulled 15 m by 200 N of
horizontal force from Joe . The coefficient
of friction between the box and the floor is
0.65. Find the work done by Joe’s force, Ff,
Fg, and FN, then find the net Work.
Comparison?
• Determine and compare the Work to move a
10kg ice block by two following methods:
– Lifting from the floor up to the 3m height
– Pushing with 49 N of force parallel to the 6m ramp
6m
3m
Uses of Work:
POWER (P)
Power is
“how fast
work is
being
done”
W
P
or P  Fv
t
Measured in Watts (W), which is Joule/sec
1 hp = 746 W
Power Example
A crane lifts a 2000 kg car to a
height of 10 m in 2.5 min.
What is the power output of that
motor?
If another crane does the same job
in 5 minutes, what is the
motor’s power?
Power Example
•
A 50 kg student climbs 5.0 m up a rope at
constant speed. If the student’s power
output is 200 W, how long does it take the
student to climb the rope? How much
work does the student do?
Power Example
• A 1,000 kg elevator carries a maximum load
of 800 kg. There is a constant frictional
force of 4,000 N resisting upward motion.
What minimum power must the motor
deliver to lift a fully loaded elevator at a
constant speed of 3 m/s?
CP Physics Chapter 5
Energy
“The ability to do Work”
Energy
• There’s many types of Energy…
But energy is energy!
Energy can change from one type
to another
All Energy is measured in Joules
We will analyze how Energy changes
• This chapter will limit Energy to Mechanical
Energy, which is Energy due to position
(potential) or motion (kinetic)
Gravitational
Potential Energy PE
• PE = Fg y
or PE = mgh
where mg = weight
and h = height
Height is relative between 2
points, typically choose
lowest point as h = 0
PE is also commonly
abbreviated with U
y or h
PE Example
A 2000 kg car is picked up by a
crane to a height of 10 m.
A) What is the PE of the car?
B) How much work was done
by the crane?
PE Example
•
A 40 kg child is in a swing that is attached
to 2 m long ropes. Find the gravitational
potential energy of the child relative to her
lowest position when:
–
–
–
The ropes are horizontal
The ropes make a 30 angle with a vertical
axis, so its is 0.27 m higher
The swing is at the bottom of the swing arc
Other potential energy
• Any time energy is stored for later use we
can call it potential energy
• Example: stretch a rubber band, or a spring,
or a bungee cord, … The energy is stored
until it is released. This is called Elastic
Potential Energy
Kinetic Energy
1 2
KE  mv
2
KE Example
• A Tennis ball and a baseball are fired from
practice machines, the tennis ball mass is 58
g and the baseball mass is 145 g. The tennis
ball is fired with a velocity of 53 m/s and
the baseball with a velocity of 35 m/s.
Which ball has more Kinetic Energy
KE Examples
•
What is the speed of a 0.045 kg golf ball if
its KE is 120 J?
•
A car has KE of 432,000 J when traveling
at a speed of 23 m/s. What is its mass?
Work-Energy Theorem
Work done on a body = Energy gained (or lost) on the body
• Net Work done by a net force acting on an
object is equal to the change in Kinetic
Energy of the object.
1
2
• Wnet = KE
F d  m ( v f
2
• Wnet = KEfinal – KEinitial
1
1
2
2
Wnet  mv f  mvi
2
2
1
1
2
2
Fnet d  mv f  mvi
2
2
 vi )
2
Work-Energy Example
•
A student wearing frictionless roller
blades is pushed by a friend with a
constant force of 45 N. How far must the
student be pushed if they start from rest
and end with a final KE of 352 J?
Work-Energy Example
•
A 2.0 x 103 kg car accelerates from rest
under the action of two forces. One force
is a forward traction force of 1,140 N and
the other is a 950 N frictional force
resisting motion. Use the work-energy
theorem to determine how far the car must
travel to reach 2.0 m/s.
Work-Energy Example
•
•
A 75 kg bobsled is pushed on a horizontal
surface starting from rest. After going a
distance of 4.5 m its speed is 6.0 m/s.
What is the net force on the sled?
If k is 0.02, what is the applied force to
cause this motion?
Law of Conservation of Energy
Total energy (Mechanical Energy) doesn’t change
Ignoring friction:
PEi  KEi  PE f  KE f
mghi 
1
2
mvi  mgh f 
2
1
2
2
mv f
http://regentsprep.org/Regents/physics/phys02/pend/default.htm
http://phet.colorado.edu/sims/pendulum-lab/pendulum-lab_en.html
Energy is path independent
: Roller coaster
Examples (no friction)
•
A 755N diver drops from a board 10.0 m
above the water surface.
–
–
–
Find the diver’s speed 5.0 m above the water
Find the diver’s speed just before entering the
water
If the diver instead went down a slide on a
25 incline, what would their speed be when
entering the water?
Example
• A bird is flying with a speed of 19.0 m/s
over water when it accidentally drops a 2.00
kg fish. If the altitude of the bird is 5.4 m
and friction is disregarded, what is the
speed of the fish when it hits the water (use
energy)
Example
•
A pendulum bob is released from some
initial height such that the speed of the
bob at the bottom of the swing is 1.9 m/s.
What is the initial height of the bob?
Example
How tall is the Steel Force roller coaster if
the train is moving at 34 m/sec at the
bottom of the first hill assuming that it
starts from 0 m/sec at the top?
How tall is the second hill on Steel Force if
the train is moving at 9 m/sec on the top?
Example
A crate slides down a 6 m long
incline of 35 degrees, so its starts
3.44 m high. How fast is it
moving at the bottom?
Conservation Of Energy with
Friction
PEi  KEi  W f  PE f  KE f
Wf = work done by friction
Remember friction does
negative Work
Wf = Ff dcos or Wf = Ff d
Ff = FN
https://www.youtube.com/watch?v=_g6Usw
iRCF0
Example
A) How much work is done by
friction when slowing a 1500 kg
car from 10 m/s to 5 m/s on a flat
road?
B) Assuming all Work is from
friction, what is  if the car takes
10 m to slow down?
Example
A 65 kg person goes down a frictionless
slide that is 15 m high, and then slides
to a stop on a horizontal landing
which has friction.
A) How fast is the person moving just as they
get to the bottom of the slide?
B) If the person stops after 30 m on the
landing, what was the friction force? What
is ?
Example
A 3kg crate slides down a 6 m long
frictionless incline of 35 degrees, 3.44 m
high. How fast is the crate going at the
bottom? If the coefficient of friction on the
floor is 0.3, how far does the crate slide?
Another crate of unknown mass slides down.
Answer the same questions about it!
Summary Problem 1
A pendulum with a length of 2.5 m has a “bob” on
the end with a mass of 1.5 kg. It is pulled to one
side 44° from its rest position (0.7 m high), then
released. Assume no friction.
a) What is its potential energy before being
released?
b) What is its maximum speed? (Where is it at
maximum speed?)
c) What is its speed on the way up when the
angle from the vertical axis is 37° (0.5 m
high)?
2
• A “ball in a bowl” is rolling with a height of
5.7 m and a velocity of 2.3m/s in a
frictionless bowl. If the ball has a mass of
1.8kg:
•
A) What maximum speed will the ball
achieve?
•
B) What maximum height will it achieve
on the other side?
3
• Given the following diagram, determine the speed
of the sphere (roller coaster) at each point (A thru
E). The track is frictionless except for the section
D-E where the coefficient of friction (k) is 0.6.
Assume the sphere starts from rest.
A
C
98 m
B
62 m
22 m
D
E
15 m
End of Chapter
Example
A crate slides to a stop when
started from 17 m/sec. If the
coefficient of friction between the
floor and crate is 0.4, how far
will it slide?
Example #4
What is the coefficient of friction
if a crate slides to the bottom of
the hill that is 8 m long and at 40
degrees. The crate is moving at 2
m/sec at the top of the incline and
it is moving at 7.5 m/sec at the
bottom?
Hooke’s Law
Fs  kx
Example
• A 5 kg mass was
placed on a relaxed
spring that is hung
vertically. The
spring displaced 3
cm. What is the
spring constant?
Elastic Potential
Energy
PEs =
2
½kx
Example #1
How much elastic potential
energy is in a spring that is
compressed 3-cm and has a
constant of 5000-N/m?
Example #2
A spring (k = 100-N/m) gets
compressed 40-cm because a 2kg object collided with it. How
fast was the object going?
Example #3
A 5 kg object is dropped onto a
spring from a height of 11 m.
A) How fast is the object moving
just before it hits the spring?
B) What spring constant is
required in order for the
spring to compress 10 cm?