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Unformatted text preview: Homework 12 Chapter 5 Questions 8, 14 & Problems 7, 16, 19, 22 Q8) What is the chance of a light car safely rounding an un-banked curve on an icy road as compared to that of a heavy car: worse, the same, or better? Assume that both cars have the same speed and are equipped with identical tires. Account for your answer. Solution: On a frictionless surface a car would not turn. The friction in between the tires and the road is what causes the car to turn. (Think of trying to turn on Ames roads during the winter, if you turn the wheel on slick ice, you continue to go straight.) So in both cases, the sum of all forces directed radially inward needs to equal mv^2/r. The only force acting inward is the force of friction. So: = = r mv F F fric 2 = mg r mv 2 gr v = As you can see, the velocity a car can maintain without slipping is independent of mass. Q14) A stone is tied to a string and whirled around in a circle at a constant speed. Is the string more likely to break when the circle is horizontal or when it is vertical? Account for your answer, assuming the constant speed is the same in each case. Solution: A string in the horizontal only experiences forces from rotation. Tension for a horizontally rotated string is: = horz T r mv 2 For the vertical case, since gravity is always pulling down, you have two extreme cases to...
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