Physics II workshop_Part_44

Physics II workshop_Part_44 - 91 Roller Coaster A roller...

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90 Using Conservation of Energy: Pendulum Consider the following pendulum set-up. A ball of mass m is attached to a string of length L , and is pulled so that the ball is an initial height h 0 from the lowest point in its swing. A rod is clamped at a height h above the lowest point so that when the pendulum swings down, the string wraps around the rod, and the ball swings around in a circle of smaller radius. Your challenge: Find the smallest height h 0 from which the ball can be released in order that it complete the small circle without the string going slack. [Hint: you will need to consider more than just energy!] Checking your answer: You will be provided a simple pendulum and can measure its length L . Set up the experiment so that the rod is at a height h = L /4. Does your predicted value succeed? Is your predicted value the "minimum"? Try decreasing the height by 5% and seeing if the ball goes around or if the string goes slack. In what ways does your actual experimental set up fall short of ideal?
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Unformatted text preview: 91 Roller Coaster A roller coaster car of total mass m =500 kg (including passengers) moves along the track shown the diagram. The track is frictionless and the car has a velocity of magnitude v 1 =2 m/s at the top of the first hill and h = 50 m. We will take the gravitational potential energy of the system to be zero at point C. Answer the following questions, using the idea of conservation of mechanical energy. Do not just write down the numerical answer — first derive and write down an equation in terms of m , g , h and v 1 , then insert the numerical values. (a) What is the total mechanical energy of the car at point A? (b) What is the gravitational potential energy (GPE) of the car at point B? (c) What is the speed of the car at point C? (d) The car will not reach the top of the last hill. How high will it go? Adapted from Cummings et al., Understanding Physics , Wiley 2006. Chapter 10 Problem 4....
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