1. Drag Forces Lecturer: Professor Stephen T. Thornton

2. Reading Quiz v R 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? R v
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3. Reading Quiz v R N mg 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, is Fc = mg – N. mg N R
Follow-up: What happens when the skier goes into a small dip?

4. Circular motion Motion on banked curves Lots of Conceptual Quizzes
Last Time
Circular motion
Motion on banked curves
Lots of Conceptual Quizzes

5. Non-uniform circular motion Drag Terminal velocity Fundamental forces
Today
Non-uniform circular motion
Drag
Terminal velocity
Fundamental forces

6. 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.]
Giancoili, 4th ed, Problem 5-59

7. 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 W T
Answer: 3

8. 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 W T
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. W T

9. Conceptual Quiz
A) car’s 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?
Answer: 2

10. Conceptual Quiz
A) car’s 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?

11. Conceptual Quiz A B C E D
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?
Answer: 2

12. Conceptual Quiz A B C E D
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 Newton’s First Law requires!
Follow-up: What physical force provides the centripetal force?

13. Conceptual Quiz
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 ball’s path, what is Fc equal to?
A) Fc = T – mg
B) Fc = T + N – mg
C) Fc = T + mg
D) Fc = T
E) Fc = mg R v
top
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14. Conceptual Quiz
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 ball’s path, what is Fc equal to?
A) Fc = T – mg
B) Fc = T + N – mg
C) Fc = T + mg
D) Fc = T
E) Fc = mg
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 the net force, therefore, is Fc = T+ mg. v T mg R

15. 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? A B C D E
Answer: 1

16. 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? A B C D E
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

17. 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.
Figure Caption: The speed of an object moving in a circle changes if the force on it has a tangential component, Ftan. Part (a) shows the force F and its vector components; part (b) shows the acceleration vector and its vector components.

18. 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.
Figure Caption: Object following a curved path (solid line). At point P the path has a radius of curvature r. The object has velocity v, tangential acceleration atan (the object is here increasing in speed), and radial (centripetal) acceleration aR (magnitude aR = v2/r) which points toward the center of curvature C.

19. Drag Forces Here, FD is the drag force; ρ the density of the medium;
A the cross-sectional area of the object;
CD the drag coefficient.
Could use coffee filter as demo.

20. 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.

21. 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).
Figure Caption: (a) Forces acting on an object falling downward. (b) Graph of the velocity of an object falling due to gravity when the air resistance drag force is FD = -bv. Initially, v = 0 and dv/dt = g, and but as time goes on dv/dt (= slope of curve) decreases because of FD. Eventually, v approaches a maximum value, vT, the terminal velocity, which occurs when FD has magnitude equal to mg.

22. Simplified Top View of a Centrifuge in Operation
Separate red and white blood cells from serum.
More dense
Less dense
Do demo of swinging tray with wine glass around vertically.

23. 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.

24. 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

25. 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 = A rope is attached to the box and pulled horizontally with tension T = 30 N. Which way does the box move? T m
Static friction (ms = 0.5 )
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26. 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 = 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. T m
Static friction (ms = 0.4 )
Follow-up: What happens if the tension is 35 N? What about 45 N?