Drag Forces Lecturer: Professor Stephen T. Thornton

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Drag Forces Lecturer Professor Stephen T.
Thornton
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Reading Quiz
A) Fc N mg B) Fc mg N C) Fc T
N mg D) Fc N E) Fc mg

• A skier goes over a small round hill with radius
  R. Because she is in circular motion, there has
  to be a centripetal force. At the top of the
  hill, what is Fc of the skier equal to?

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Reading Quiz
A) Fc N mg B) Fc mg N C) Fc T
N mg D) Fc N E) Fc mg

• A skier goes over a small round hill with radius
  R. Because she is in circular motion, there has
  to be a centripetal force. At the top of the
  hill, what is Fc of the skier equal to?

v
Fc points toward the center of the circle (i.e.,
downward in this case). The weight vector points
down and the normal force (exerted by the hill)
points up. The magnitude of the net force,
therefore, isFc mg N.
N
mg
R
Follow-up What happens when the skier goes into
a small dip?
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Last Time

• Circular motion
• Motion on banked curves
• Lots of Conceptual Quizzes

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Today

• Non-uniform circular motion
• Drag
• Terminal velocity
• Fundamental forces

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• Banked Curve. A curve of radius 68 m is
  banked for a design speed of 85 km/h. If the
  coefficient of static friction is 0.30 (wet
  pavement), at what range of speeds can a car
  safely make the curve? Hint Consider the
  direction of the friction force when the car goes
  too slow or too fast.

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Conceptual Quiz

• In the game of tetherball, the struck ball
  whirls around a pole. In what direction does the
  net force on the ball point?

A) toward the top of the pole B) toward the
ground C) along the horizontal component of the
tension force D) along the vertical component of
the tension force E) tangential to the circle
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Conceptual Quiz
In the game of tetherball, the struck ball
whirls around a pole. In what direction does the
net force on the ball point?

A) toward the top of the pole B) toward the
ground C) along the horizontal component of the
tension force D) along the vertical component of
the tension force E) tangential to the circle
The vertical component of the tension balances
the weight. The horizontal component of tension
provides the centripetal force that points toward
the center of the circle.
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Conceptual Quiz
A) cars engine is not strong enough to keep
the car from being pushed out B) friction between
tires and road is not strong enough to keep car
in a circle C) car is too heavy to make the
turn D) a deer caused you to skid E) none of the
above

• You drive your car too fast around a curve and
  the car starts to skid. What is the correct
  description of this situation?

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Conceptual Quiz
A) cars engine is not strong enough to keep the
car from being pushed out B) friction between
tires and road is not strong enough to keep car
in a circle C) car is too heavy to make the
turn D) a deer caused you to skid E) none of
the above

• You drive your car too fast around a curve and
  the car starts to skid. What is the correct
  description of this situation?

The friction force between tires and road
provides the centripetal force that keeps the car
moving in a circle. If this force is too small,
the car continues in a straight line!
Follow-up What could be done to the road or car
to prevent skidding?
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Conceptual Quiz

• A Ping-Pong ball is shot into a circular tube
  that is lying flat (horizontal) on a tabletop.
  When the Ping-Pong ball leaves the track, which
  path will it follow?

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Conceptual Quiz

• A Ping-Pong ball is shot into a circular tube
  that is lying flat (horizontal) on a tabletop.
  When the Ping-Pong ball leaves the track, which
  path will it follow?

Once the ball leaves the tube, there is no
longer a force to keep it going in a circle.
Therefore, it simply continues in a straight
line, as Newtons First Law requires!
Follow-up What physical force provides the
centripetal force?
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Conceptual Quiz
A) Fc T mg B) Fc T N mg C) Fc
T mg D) Fc T E) Fc mg

• You swing a ball at the end of string in a
  vertical circle. Because the ball is in circular
  motion there has to be a centripetal force. At
  the top of the balls path, what is Fc equal to?

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Conceptual Quiz

A) Fc T mg B) Fc T N mg C) Fc
T mg D) Fc T E) Fc mg
You swing a ball at the end of string in a
vertical circle. Because the ball is in circular
motion there has to be a centripetal force. At
the top of the balls path, what is Fc equal to?
Fc points toward the center of the circle (i.e.,
downward in this case). The weight vector points
down and the tension (exerted by the string)
also points down. The magnitude of thenet force,
therefore, is Fc T mg.
v
T
mg
R
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Conceptual Quiz

• A rider in a barrel of fun finds herself stuck
  with her back to the wall. Which diagram
  correctly shows the forces acting on her?

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Conceptual Quiz

• A rider in a barrel of fun finds herself stuck
  with her back to the wall. Which diagram
  correctly shows the forces acting on her?

The normal force of the wall on the rider
provides the centripetal force needed to keep her
going around in a circle. The downward force of
gravity is balanced by the upward frictional
force on her, so she does not slip vertically.
See http//physics.bu.edu/duffy/semester1/semeste
r1.html
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Nonuniform Circular Motion
If an object is moving in a circular path but at
varying speeds, it must have a tangential
component to its acceleration as well as the
radial one.
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Nonuniform Circular Motion
This concept can be used for an object moving
along any curved path, as any small segment of
the path will be approximately circular.
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Drag Forces
Here, FD is the drag force ? the density of the
medium A the cross-sectional area of the
object CD the drag coefficient.
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Velocity-Dependent Forces Drag and Terminal
Velocity
When an object moves through a fluid at low
speed, it experiences a drag force that depends
on the velocity of the object. For small
velocities, the force is approximately
proportional to the velocity for higher speeds,
the force is approximately proportional to the
square of the velocity.
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If the drag force on a falling object is
proportional to its velocity, the object
gradually slows until the drag force and the
gravitational force are equal. Then it falls with
constant velocity, called the terminal velocity
(120 mph for humans).
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Simplified Top View of aCentrifuge in Operation
Separate red and white blood cells from serum.
More dense Less dense
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Centrifuges

• Centrifuges have many uses.
• Separating red and white blood cells from serum.
• Separating 235U from 238U to produce fissionable
  material.
• Separating large molecules from smaller molecules
  for research and pharmaceutical purposes.

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• Fundamental Forces
• Universal gravitation gravitational force
  between any two masses
• Electroweak force includes electric, magnetic,
  and weak nuclear forces (responsible for
  radioactive decay)
• Strong (nuclear) force binds protons and
  neutrons together in nucleus

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Conceptual Quiz
A) moves to the left B) moves to the right C)
moves up D) moves down E) the box does not
move

• A box of weight 100 N is at rest on a floor
  where ms 0.4. A rope is attached to the box
  and pulled horizontally with tension T 30 N.
  Which way does the box move?

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Conceptual Quiz
A) moves to the left B) moves to the right C)
moves up D) moves down E) the box does not
move

• A box of weight 100 N is at rest on a floor
  where ms 0.4. A rope is attached to the box
  and pulled horizontally with tension T 30 N.
  Which way does the box move?

The static friction force has a maximum of msN
40 N. The tension in the rope is only 30 N.
So the pulling force is not big enough to
overcome friction.
Follow-up What happens if the tension is 35 N?
What about 45 N?