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3. Twirl one stopper, but this time change the length of the string.
- a) Write down a description of what you observed concerning the length of the string and the force on your fingers.
- b) What properties of the twirling stopper must you hold constant if you wish to compare only how changes in length affect the required force?
4. Transfer your observations about the cork on the string to your area of interest for the Chapter Challenge—roller coasters. To keep a roller coaster moving in a circle requires a force toward the center of the circle. The wheels on the track, the surface of the track, or the force of gravity can supply this force.
- a) How does the required force change when the speed of the roller coaster changes?
- b) How does the required force change when the mass of the roller coaster changes?
- c) How does the required force change when the radius of the curve changes?
- d) If the speed of a roller coaster were increased, how might you strengthen the track to provide the additional force required?
5. In physics, scientists often look at "limiting cases" to help them understand a concept better. A limiting case is the most extreme case that you may imagine. For instance, analyze the limiting cases for a roller coaster going around a horizontal curve that is not banked. If the car's speed got larger and larger and larger, the limiting case would be an infinite speed.
- a) If the cart were going at an infinite speed, how large a frictional force would be required by the track to keep the cart moving in the curve? Write your response down in your Active Physics log.
- b) The other limiting case is a car with zero speed. How large a frictional force would the track have to provide if the cart were moving very, very, very, slowly around a curve? Write your response down in your Active Physics log.
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