Romantic Turn

1
Romantic Turn

• You are driving with a friend who is sitting to
  your right on the passenger side of the front
  seat. You would like to be closer to your
  friend and decide to use your knowledge of
  physics to achieve your romantic goal. So you'll
  make a sharp turn. Which direction should you
  turn so as to make your friend slide closer to
  you? If the coefficient of static friction
  between your friend and the seat of the car is
  0.40, and you drive at a constant speed of 18
  m/s, what is the maximum radius you could make
  your turn and still have your friend slide your
  way?

2
Project

• Sweep a bowling ball around a chair with a broom.
• Which way do you sweep to keep the ball moving in
  a circle?
• Why?
• What does the bowling ball want to do?

3
Lesson 72Topic Circular Motion
5/8/07

• Objectives (After this class I will be able to)
• 1. Describe and explain centripetal acceleration
  and force.

Warm Up A merry-go-round has a radius of 6m and
makes a full rotation every 5 seconds. What is
the speed of a horse on the outer edge of the
ride?
Assignment Concept Development 9-2
4
A merry-go-round has a radius of 6m and makes a
full rotation every 5 seconds. What is the speed
of a horse on the outer edge of the ride?

1. 1.2m/s
2. 2.4m/s
3. 7.5m/s
4. 30m/s

5
Tangential Velocity

• A horse on a merry-go-round has velocity tangent
  to the circle.
• Its velocity is always perpendicular to the
  radius of the circle.

r
v
6
Rotate vs. Revolve

• Rotation An object spinning around a point
  located within the object.
• Example The Earth rotates about its axis.
• Revolution An object moving in a circle around a
  point in space.
• Example The Earth revolves around the Sun.

7
Centripetal Force

• An object in motion will stay in motion in a
  straight line unless acted on by an outside
  force.
• This means that a force must be acting on an
  object that is moving in a circle.
• The force causing an object to move in a circle
  is called the Centripetal Force.
• Centripetal center seeking.
• demo

8
Centripetal Force
9
Centripetal Acceleration

• Acceleration an object speeding up, slowing
  down, or changing direction.
• An object moving in a circle is constantly
  changing direction.
• Centripetal force causes the object to accelerate
  towards the center of the circle.
• The tangential velocity prevents the object from
  going straight towards the center.
• Example Moon around Earth

10
Centripetal Acceleration
11
Centripetal Acceleration Equation
a centripetal acceleration v tangential
velocity r radius
Centripetal Force Equation
12
A runner moving at a speed of 8.8m/s rounds a
bend with a radius of 25m. What is the
centripetal acceleration of the runner?

1. 0.352m/s2
2. 3.10m/s2
3. 3.10m/s

13
An airplane traveling at 201 m/s makes a turn.
What is the smallest radius of the circular path
(in km) that the pilot can make and keep the
centripetal acceleration under 5.0 m/s2?

1. 8080.2 km
2. 40.2 km
3. 8.08 km
4. 7820.6 km

14
A 45 kg merry-go-round worker stands on the
rides platform 6.3 m from the center. If her
speed as she goes around the circle is 4.1 m/s,
what is the force of friction necessary to keep
her from falling off the platform?

1. 29.29 N
2. 120.07 N
3. 29.29 m/s2
4. 120.07 m/s2

15
A car racing on a flat track travels at 22 m/s
around a curve with a 56 m radius. Find the
cars centripetal acceleration. What minimum
coefficient of static friction between the tires
and road is necessary for the car to round the
curve without slipping?

1. 8.64
2. 864.29 m/s2
3. .86 N
4. .86

16
Project

• List objects that move in circles.
• List what is causing the centripetal force for
  each object.
• Describe the Romantic Turn and what the maximum
  radius can be and yet still achieve your goal.
  (Would this trick ever actually work on anyone?)

17
Lesson 73Topic Lab Circular Motion
4/30/07

• Objectives (After this class I will be able to)
• Solve for the tangential velocity of a whirling
  object.
• Calculate for the mass of a rubber stopper using
  the centripetal force equation.

Lab Task Find the mass of a rubber stopper using
Fcmv2/r
Assignment Lab Report due tomorrow (show all
calculations!)
18
Croc Dundee Noisemaker

• After watching the movie "Crocodile Dundee," you
  and some friends decide to make a communications
  device invented by the Australian Aborigines. It
  consists of a noise-maker swung in a vertical
  circle on the end of a string. Your design calls
  for a 400 gram noise-maker on a 60 cm string. You
  are worried about whether the string you have
  will be strong enough, so you decide to calculate
  the tension in the string when the device is
  swung with an acceleration which has a constant
  magnitude of 20 m/s2 . You and your friends can't
  agree whether the maximum tension will occur when
  the noise maker is at the highest point in the
  circle, at the lowest point in the circle, or is
  always the same. To settle the argument you
  decide to calculate the tension at the highest
  point and at the lowest point and compare them.

19
Project

• Loop the loop track
• Describe what makes the ball make it around the
  loop.
• Draw the forces acting on the ball at the top of
  the loop and at the bottom of the loop.

20
Lesson 74Topic Non-Uniform Circular Motion
4/31/07

• Objectives (After this class I will be able to)
• 1. Describe inertial and non-inertial reference
  frames.
• 2. Define Centrifugal Force.
• 3. Solve problems involving Non-Uniform circular
  motion.

Warm Up A 615kg racecar completes one lap in
14.3s around a circular track with a radius of
50m. The car moves at constant speed. What is the
acceleration of the car?
Assignment Non- Uniform Circular motion
21
A 615kg racecar completes one lap in 14.3s around
a circular track with a radius of 50m. The car
moves at constant speed. What is the acceleration
of the car?

1. 9.65m/s2
2. 0.44m/s2
3. 0.24m/s2
4. 0 m/s2

22
Inertial Reference Frame

• Inertial Reference Frame explanations of
  observations where Newtons laws hold true.
• Example Watching a car race on a circular track.
  Friction is the centripetal force accelerating
  the cars towards the center of the track.

23
Non-Inertial Reference Frame

• Non-Inertial Reference Frame an imaginary force
  needs to exist for Newtons laws to hold true.
• Example Being in a car going around a circular
  race track. You feel pushed towards one side of
  the car.
• You can say that this push is some imaginary
  force rather than the inertia of your body.
• This imaginary force is called the centrifugal
  force.
• Centrifugal center fleeing

24
Non-Uniform Circular Motion

• The motion of an object is non-uniform when other
  forces are acting on it besides the centripetal
  force.
• Example An object moving in a vertical circle.

25
Non-Uniform Circular Motion Problems

• When solving non-uniform problems, Fnet 0 and
  use centrifugal force instead of centripetal
  force.
• Example A roller coaster car speeds down a hill
  past point A and then rolls up a hill past point
  B
• a. The car has a speed of 20m/s at point A. If
  the normal force is 20600N at this point, what is
  the mass of the car?

26
Non-Uniform Circular Motion Problems

• Example A roller coaster car speeds down a hill
  past point A and then rolls up a hill past point
  B
• b. What is the maximum speed the car can have at
  point B for the gravitational force to hold it on
  the track?

r 15m
27
A carnival clown rides a motorcycle down a ramp
and around a vertical loop. If the loop has a
radius of 18m, what is the slowest speed the
rider can have at the top of the loop to avoid
falling?

1. 4.24m/s
2. 13.4m/s
3. 18m/s
4. 180m/s

28
A 1.13kg ball is swung vertically from a 0.5m
cord in circular motion at a speed of 2.4m/s.
What is the tension in the cord at the bottom of
the balls motion?

1. 11.3N
2. 13.0N
3. 24.3N
4. 1.7N

29
A mythical warrior swings a 5.6kg mace on the end
of a magically massless 86cm chain in a
horizontal circle above his head. The mace makes
one full revolution in 1.8s. Find the tension in
the magical chain.

1. 1.49N
2. 58.7N
3. 5868N
4. 28.0N

30
Croc Dundee Noisemaker

• Find the tension in the noisemaker at both top
  and bottom of the vertical circle.

31
Bonus

• A passenger train traveling at constant speed
  rounds a curve of radius 275m. A chandelier
  suspended from the ceiling swings out to an angle
  of 17.5 throughout the turn. What is the speed
  of the train?