Kinetic and Potential Energy Problems

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	2.1) Wingardium Leviosa* In Harry Potter and the Sorcerer’s Stone by J.K. Rowling, Ron Weasley manages to knock a troll out by levitating its club and then dropping the club on the troll’s head. If the troll is 12 feet tall and Ron manages to drop the club, weighing 50 kg, from 15 feet in the air, how much kinetic energy will it transfer to the trolls head when it strikes? If the troll’s head brings the club to a complete stop before it continues to the floor, how fast will the club be moving when it hits the floor? 2.2) Valentina’s Flight The first woman in space, cosmonaut Valentina Tereshkova, flew in 1963. She orbited the earth 48 times during her 70 hour 50 minute flight at an average altitude of 165.5 km above the surface of the earth. Her spacecraft, Vostok 6, had a mass of about 4700 kg. What was her average kinetic energy in this flight? What was her average gravitational potential energy? Is she high enough that the gravitational field strength is different from what it is on the surface of the earth)? 2.3) Aswan High Dam The Aswan High Dam in Egypt, built from 1960 to 1970, is an engineering masterpiece, though it has caused environmental and cultural problems in the surrounding area. It increased the amount of cultivatable land in Egypt by 30% and produces 2.1 GW of power, but over 90,000 people were displaced by Lake Nasser, the reservoir formed by the dam. Also, about 12% of the water held in the lake is lost to evaporation. This enormous structure generates power by letting the waters of the Nile fall from a height of 111 m. How much water goes over the dam each second? How fast is the water falling when it reaches the base of the dam? Top 2.4) Visit to Vesta** STScI You are the first person to set foot on the asteroid Vesta, on of the largest asteroids in the solar system with a mass of 3.0 x 10²⁰ kg and a radius of 265.5 km. While taking pictures from the asteroids surface, you drop your camera. How fast is it moving when it hits the ground? After gathering all of the information and pictures you need, you climb back into your spaceship to go home. How fast must you take off to escape the asteroid’s gravitational pull? 2.5) Making a Skirt* Erika is sewing a 75 cm piece of elastic into the waist of a skirt she is making. After she has threaded it through the skirt and stitched the two ends of the elastic together, she notices that when she holds up the skirt by the elastic alone the loop stretches 3 cm towards the floor. If the fabric of the skirt has a mass of .5 kg, what is the spring constant of the elastic? Sarah Matthews How much potential energy does the elastic have when she pulls the skirt on over her head, stretching its circumference to 90 cm? 2.6) Bungee Race*** Between periods of hockey games, bungee races are a fun but silly way to keep the crowd entertained. A few lucky fans get hooked to bungee cords and have to run across the ice to retrieve their prizes. Of course, they tend to lose their footing and get pulled back to the starting point. Tom, whose mass is 80 kg, is selected to participate. He runs across the ice and manages to stretch the bungee cord, with a spring constant of 100 N/m, 3 m longer than its normal length of 5 m before falling. How much work did he do on the bungee cord? The coefficient of friction between the ice and his pants is .08. What is the fastest backward speed he attains? At what point does he stop moving backwards? How much work did the bungee cord do on him? Top Energy Problems

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