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U9 WS 3 – Rollercoasters (Energy and Circular Motion) NAME_________________________ Per__ Below is part of the track on a roller coaster ride that you are riding. You are in motion at all points A-H B 1. A. If it takes 0.1 seconds for you to pass through one meter of track at point B, how fast are you going at point B? What direction is your velocity at point B? F 12m A C G D 6m E H B. What size and in what direction is your acceleration at point B? 2. A. Calculate the net force on you at point B (your mass is 80 kg). B. Draw a force diagram for you at point B. Calculate the size of all the forces on you at point B and put these amounts on your force diagram. 3. A. If point B is 28 meters higher than point D, how fast must you be going at point D (Assume no energy is dissipated between B and D)? (hint: think energy!) B. Are you accelerating at point D? If so, in which direction and how much? ( Hint: figure out the radius.) C. Draw a force diagram for you at point D. Calculate the size of all the forces on you at point D and put these amounts on your force diagram. 4. Suppose you have enough speed to just make it past point F without falling off the track. A. Draw a force diagram to represent this situation. B. Determine the minimum velocity needed to make it through the loop. (Hint: use your force diagram) C. Calculate your acceleration at point F. 5. A. How fast must you be going at point H, if 10 % of the energy you started with is dissipated during your trip? B. Draw a force diagram for you at point H. 6. Sally has a mass of 40 kg. She rides the Ferris wheel as the wheel rotates at a constant speed. She uses her fancy wristwatch to determine that it takes 12.57 seconds for her to make a complete trip around the wheel. r = 4.5 m A A. Determine the speed and acceleration of Sally at any point on the wheel. C B B. Force diagrams: Draw quantitative force diagrams -- one for the net force, one for the individual forces -- for Sally at the three locations. A. B. C. Force Diagram Force Diagram Force Diagram Net Force Diagram Net Force Diagram Net Force Diagram 7. At what constant speed would the 80 kg driver pictured below have to be traveling in order to feel twice his normal body weight as he drives into a depression in the road with a radius of curvature of 20 meters. Be sure to draw a force diagram to represent the situation before you even attempt to solve the problem. Hint: which force affects how much weight you feel that you have? r = 20m