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Assignment 2 Centripetal Force & Univ LAST NAME______________________________ FIRST NAME_____________________DATE______ CJ - Assignment 2 Centripetal Force & Universal Gravitation, 5.4 Banked Curves Draw the vectors for a free body diagram of a car in an unbanked turn and a banked turn. For this situation assume the cars are turning to the left side of the drawing. Car in Unbanked Turn Car in Banked turn Is this car in Equilibrium? Is this car in Equilibrium? Do the same for the airplane. Airplane in Unbanked Turn Airplane in Banked turn Let’s be careful to fully understand what is going on with this one. We have made an assumption in doing this for the airplane which are not valid. THE BANKED TURN- car can make it a round a turn even if friction is not present (or friction is zero). In order for this to happen the curved road must be “banked”. In a non-banked turn the centripetal force is created by the friction of the road on the tires. What creates the centripetal force in a banked turn? Imagine looking at a banked turn as shown to the right. Draw the forces that act on the car on the diagram of the car. Is the car in Equilibrium? YES , NO The car which has a mass of m is travelling at a velocity (or speed) v around a turn of radius r. How do these variables relate to optimize the banked turn. If the mass of the car is greater is a larger or smaller angle required? LARGER, SMALLER, NO CHANGE NECESSARY If the VELOCITY of the car is greater is a larger or smaller angle required? LARGER, SMALLER, NO CHANGE NECESSARY If the RADUS OF THE TURN is greater is a larger or smaller angle required? LARGER, SMALLER, NO CHANGE NECESSARY To properly show the relationship an equation must be created. OPTIMIZING A BANKED TURN. DRAW THE FBD (without components) Is car in Equilibrium in Vertical Axis? Yes / No Apply appropriate Law for Vert Axis, (ΣF=0 or ΣF=ma) to determine Equivalent of Vertical Component of Normal Force Is car in Equilibrium in Horizontal Axis? Yes / No Apply appropriate Law for Horizontal Axis, (ΣF=0 or ΣF=ma) to determine Equivalent of Horizontal Component of Normal Force DRAW THE FBD (with vert & horizontal components of Normal Force) Create a Ratio of the Horizontal Comp / Vertical Comp Simplify Conceptual Questions 6, 7, 8, 9, 11– 155 page 6. Other things being equal, would it be easier to drive at a high speed around and unbanked horizontal curve on the moon that to drive around the same curve? (Explain why or why not) 7. A bug lands on a windshield wiper. Explain why the bug is more likely to be dislodged when the wipers are turned on at the high rather than low setting. 8. What is the chance of a light car safely rounding an unbanked turn on an icy road as compared to that of a heavy car: worse, the same or better? Assume both cars have the same speed and are equipped with identical tires. Explain your answer. 9. A container filled with water can attached to a rope. Holding the free end of the rope, you whirl the container in a horizontal circle at constant speed. There is a hole in the container, so that as you whirl it, water continually leaks out. Explain what, if anything, you feel as the water leaks out. 11. A penny is placed on a rotating turntable. Where on the turntable does the penny require the largest centripetal force such that it does not begin to slide on the surface. Problems 20, 22, 25, 26 page 157 20. Two banked curves have the same radius. Curve A is banked at an angle of 13 degrees and Curve B is banked at 19 degrees. A car can travel around A without relying on friction at a speed of 18 m/s. At what speed can this car travel around curve B without relying on friction? 22. On a banked race track, the smallest circular path on which cars can move has a radius of 112 m., while the largest has a radius of 165 m. The height of the outer wall is 18 m. Find the smallest and largest speed at which cars can move on this track without relying on friction. 25. A jet (m = 200,000 kg), flying at 123 m/s, banks to make a horizontal circular turn. The radius of the turn is 3810 m. Calculate the necessary lift force. 26. The drawing shows a baggage carousel at an airport. Your suitcase has not slid all the way down the slope and is going around at constant speed on a circle (r = 11 m) as the carousel turns. The coefficient of static friction between the suitcase and the carousel is .760, and the angle theta in the drawing is 36 degrees. How much time is required for your suitcase to go around once? .
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