1. Aim: How do we explain centripetal motion?

2. THOUGHT QUESTION 1
The figure shows the path of a park ride that travels at constant speed through five circular arcs of radii R0, 2R0, and 3R0. Rank the arcs according to the magnitude of the centripetal force on a rider traveling in the arcs, greatest first.
Fc=mv2/r
The smaller the radius is, the greater the centripetal force.
So 4>3>1=2>5

3. THOUGHT QUESTION 2
A person riding a ferris wheel moves through positions at (1) the top, (2) the bottom, and (3) midheight. If the wheel rotates at a constant rate, rank these three positions according to (a) the magnitude of the person’s centripetal acceleration, (b) the magnitude of the centripetal force on the person, and (c) the magnitude of the normal force on the person, greatest first.

5. Problem 1-How Fast can it spin?
An object of mass kg is attached to the end of a cord whose length is 1.50 m. The object is whirled in a horizontal circle. a) If the cord can withstand a maximum tension of 50 N, what is the maximum speed of the object can have before the cord breaks? b) Calculate the tension in the cord if the speed of the object is 5.00 m/s
a) 12.2 m/s b) 8.33 N

6. Problem 1

8. Problem 2-The conical pendulum
A small object of mass m is suspended from a string of length L. The object revolves in a horizontal circle of radius r with constant speed v. (Because the string sweeps out the surface of a cone, the system is known as a conical pendulum.) Find (a) the speed of the object, and (b) the period of revolution, defined as the time needed to complete one revolution.
a) v =√(Lgsinθtanθ) b) T = 2π√(Lcosθ/g)

9. Problem 2

10. Problem 2

12. Problem 3-What is the maximum speed of the car?
A 1500 kg car moving on a flat, horizontal road negotiates a curve whose radius is 35.0 m.
If the coefficient of static friction between the tires and the dry pavement is 0.500, find the maximum speed the car can have in order to make the turn successfully.
On a wet day, the car described in this example begins to skid on the curve when its speed reaches 8.00 m/s. What is the coefficient of static friction in this case?
a) 13.1 m/s b) 0.187

13. Problem 3

14. Problem 3

16. Problem 4
A pilot of mass m in a jet aircraft executes a “loop-the-loop” maneuver. The aircraft moves in a vertical circle of radius 2.70 km at a constant speed of 225 m/s. Determine the force exerted by the seat on the pilot at (a) the bottom of the loop and (b) the top of the loop. Express the answers in terms of the weight mg of the pilot.
a) 2.91 mg b) mg

17. Problem 4