Transcript PHY160-17S

TODAY’S OUTCOMES:
FORCE, MOTION AND ENERGY
- Review energy and discuss how
energy is conserved and changes forms
- Investigate how energy works in
pendulums and springs
- Study the force of friction on a wooden
block
Suppose a barge carrying 100,000 kg of coal (a bit more than 100 tons) is moving down the Ohio river at 10 m/sec when it is
noticed that there is a fishing boat in the channel, 100 meters away. What force does the barge need to exert to stop before it
hits the fishing boat?
Solve this problem using 2 different methods:
Method 1: Using the 3 Laws of Motion
a) If the barge is to attain the speed of 0 m/sec when it reaches the boat, what will its average speed be?
Average speed = ½ × Initial speed = 5 m/sec
b) With this average speed, how much time will it take the barge to cover the distance between it and the boat?
speed = distance / time
time = distance / speed
c) Given this time and the initial
speedmof/ 5
10m/sec
m/sec, what acceleration must the barge have to stop in time?
= 100
= 20 sec
d) Using the Lawacceleration
of Force and Acceleration,
what
force /istime
required on the barge?
= change in
speed
= 10 m/sec / 20 sec
= 0.5 m/sec2
Force = mass × acceleration
= 100,000 kg × 0.5 m/sec2
= 50,000 Newtons
Suppose a barge carrying 100,000 kg of coal (a bit more than 100 tons) is moving down the Ohio river at 10 m/sec when it is
noticed that there is a fishing boat in the channel, 100 meters away. What force does the barge need to exert to stop before it
hits the fishing boat?
Method 2: Using the Conservation of Energy
e) What is the kinetic energy of the moving barge?
Kinetic energy = ½ mass × (velocity)2
= 0.5 × 100,000 kg × (10 m/sec)2
= 5,000,000 Joules
f) Using conservation of energy, what force is needed to stop the barge before it hits the boat?
Energy = Force × distance
Force = Energy / distance
= 5,000,000 Joules / 100 m
= 50,000 Newtons
- In this (and other examples), we saw the energy at
the start was the energy at the finish.
- Another way to state this is to say energy was
conserved.
2 meters
You applied this principle in
the last lab, when raising and
dropping a metal ball.
A 0.005 kg (0.05 N) ball resting on
the ground has zero energy.
- In this (and other examples), we saw the energy at
the start was the energy at the finish.
- Another way to state this is to say energy was
conserved.
2 meters
You applied this principle in
the last lab, when raising and
dropping a metal ball.
Raising the ball 2 meters gives the
ball potential energy
energy = force × distance
= 0.05 N × 2 m = 0.1 Joules
- In this (and other examples), we saw the energy at
the start was the energy at the finish.
- Another way to state this is to say energy was
conserved.
You applied this principle in
2 meters
the last lab, when raising and
dropping a metal ball.
As the ball accelerates, the potential
energy becomes kinetic energy
Halfway down, the distance of the
ball is half what it started, so it has
only half its potential energy - the
rest is now kinetic energy (½mv2).
- In this (and other examples), we saw the energy at
the start was the energy at the finish.
- Another way to state this is to say energy was
conserved.
You applied this principle in
2 meters
the last lab, when raising and
dropping a metal ball.
At the bottom, the potential energy
is again zero - it has all become
kinetic energy.
So, kinetic energy = ½mv2 should
be equal to the potential energy of
0.1 Joules.
This example assumes energy is conserved - is
energy always conserved? (That is, can you create or
destroy new energy?)
You’ve heard since you were a young child in
science class: ENERGY CANNOT BE CREATED OR
DESTROYED.
However - is energy always conserved within the
system you are measuring?
Back to the falling ball example:
2 meters
What happens AFTER the ball hits the
ground? Does it still have stored energy
or kinetic energy?
The ball bounced a bit, so it had
some kinetic energy left.
What about when the ball comes to a
complete rest? Where did the energy
“go”?
Some went into sound, some went into
heat. Energy in the whole room is
conserved, but things like friction can
cause energy to leave the system you
are measuring.
WHAT YOU ARE EXPECTED TO KNOW:
- Potential energy is given by force × distance,
and (in the absence of friction) does not depend
on the path taken
- Potential energy can be changed into kinetic
energy
- Solve problems involving force, mass and
distance using kinetic and potential energy
19. A railway freight car is coasting on a level track with a small velocity (a few meters per second). A very strong man
is trying to stop it by pulling on a rope. Which statement is correct?
A) The man can stop the freight car, but he has to do so over a long distance.
B)
The man will not stop the car unless the force is larger than the weight of the freight car.
C) The man will not stop the car unless the force is greater than the kinetic energy of the fright car.
D) No matter how strong the man is, he will not be able to stop the freight car.
A) is the correct answer. The moving freight car
has a large kinetic energy. The man needs to take
this energy away from the car.
Energy = Force × distance, and since his force on
the car is (relatively) small, he will need a long
distance to stop the car.
20. a) If a 5 kg goose flying south at 40 m/sec encounters a 1,000,000 kg jet plane flying north at 200 m/sec, how is the force of the
goose on the jet plane related to the force of the jet plane on the goose?
According to the Law of Interaction, the forces are equal and opposite!
MASS OF PLANE
Force on plane = – Force on goose
× acceleration of plane = – mass of goose × ACCELERATION
OF GOOSE
b) Suzanne observes that the goose gets smashed flat and the airplane hardly changes speed at all. Terry concludes from this that the force
of the airplane on the goose must be much larger than the force of the goose on the airplane. Using considerations of energy, please reconcile
Suzanne's observation with your answer to Q. 20 (that is explain
how both you and Suzanne are right, whether you agree with Terry or not).
2
Kinetic energy = ½ mass × (velocity) , so the more massive plane has MUCH more
kinetic energy than the goose, so the plane is unharmed while the goose is squashed
flat!
22. a) A 1.5-Newton hockey puck slides 50 meters on ice. How much energy does it use? (Look back at the definition of energy before
answering....)
Energy = Force × distance, and the force must act along the direction of motion!
1.5 N is a weight pulling downward - there is no acceleration in the direction of motion
(horizontal), so there is no energy used!
b) A goalie catches the puck in his glove, exerting a 50,000-Newton force over a distance of 2 cm. How much energy is absorbed by his
glove?
Energy = Force × distance
= 50,000 N × 0.02 m
= 1000 J
23. So far, you have seen that, for all machines, energy in = energy out. Consider the
example of a windlass (pictured right) composed of a crank handle and a rope wrapped
around an axle. Here, the bucket weighs 30 Newtons, the radius of the axle is 10 cm (0.1 m)
and the handle length is 40 cm (0.4 m).
a) The circumference of a circle is 2 ✕ π ✕ radius. Find both the circumference of the axle,
and the total distance your hand would move in one complete turn of the crank (that is, the
circumference).
daxle = 2 × 3.14 × 0.1 m = 0.62 m
dhandle = 2 × 3.14 × 0.4 m = 2.51 m
b) Use your answer to a) to determine how far your hand would have to move to lift the
bucket 1 meter.
1 meter of rope wraps around the axle - the handle has to turn
once every time the axle turns once.
dhandle/daxle = 2.51 / 0.62 = 4
The handle must be pushed 4 m for every 1 m of rope.
c) If energy in = energy out, what force is required to turn the crank handle to lift the 30-N
bucket?
Energy = Force × distance
Energybucket = 30 N × 1 m = 30 J
Energyhandle = ? × 4 m = 30 J
? = 7.5 N
TODAY’S OUTCOMES:
FORCE, MOTION AND ENERGY
- Review energy and discuss how
energy is conserved and changes
forms✓
- Investigate how energy works in
pendulums and springs
- Study the force of friction on a wooden
block