# What is the kinetic energy at the bottom of the fall?

Your assignment is to solve these ten problems. The most important portion of your grade is going to be showing you work rather than just the final answer. That is, you cannot receive full credit on this assignment if you only put the final answers, even if they are correct. I would ask that you number each problem and keep them at least marginally organized for my own sanity. You might also consider writing very short descriptions of the steps you’re taking as part of your reasoning and work. You are welcome to work with others on this, but I’d ask that everyone submit their own work. There will be a discussion opened for this assignment if you’d like to go over the steps you’re taking or find some classmates to work with.An object with 2 kilograms of mass is lifted into the air by 4 meters. The object is dropped. What is the kinetic energy at the bottom of the fall? What is the final velocity just before it hits the ground? – 8.85m/sHow much work does a 70-kg person do running up a mountain with a vertical rise of 2,500 feet (760 m)? Express the answer in both Joules and kilocalories. If the run takes 50 minutes, what’s the average power involved? – 124.6kcal, 173.8WIn 2010 a well being frilled from the Deepwater Horizon platform in the Gulf of Mexico blew out, spilling some 5 million barrels of oil into the water over 3 months. (Maybe you saw the movie?) (a) Find the energy equivalent of the spilled oil, in joules, and (b) estimate how long this oil could have supplied the entire power demand of the USA, 2.8 x 1012 W. – ~3 hoursA car with a mass of 1700 kg can go from rest to 100 km/h in 8 seconds. If its energy increases at a constant rate, how much power must be applied to achieve this acceleration? Give your answer in horsepower. – 110hpThere’s a claim that buying an SUV instead of a standard car wastes as much energy as leaving your refrigerator door open for 7 years. Extraordinary claims require extraordinary evidence. Let’s test it ourselves.A typical refrigerator (not our energy efficient one) consumes energy at a rate of about 400W while running. While normal refrigerators don’t run all the time, ours will because we’re leaving the door open. Assume that your average SUV has a fuel efficiency of 20 miles per gallon. The average car has an efficiency of 30 miles per gallon. Each gallon of gasoline contains 40kWh of energy per gallon, and let’s say you drive 15,000 miles in a year. In a single year, how many years would you have to leave your refrigerator door open to match the energy difference between the two vehicles? – 2.85 yearsA typical indoor temperature is typically around 68ºF. What is this temperature in Celsius? In Kelvin? – 293KImagine you’re making some decisions about how you’d like to build the basement of a house. In total, the walls have a total surface area of 1000 ft2, and you expect the basement will be around 70ºF inside but the outside temperature is 45ºF. If the walls were made only of concrete (R = 1.1 ft2・ºF・h / Btu), what would be the rate of heat lost through the walls? If you added an insulating material like blueboard (R = 5 ft2・ºF・h / Btu) to the concrete, what would be the new and improved rate of heat loss? – 4098 Btu/hA block of concrete that has a mass of 2kg is allowed to cool down from 40ºC to room temperature, 20ºC (that’s a hint for problem 1). If the specific heat of concrete is 920 J/kg K, how much heat is released during this process? – 36,800JThe electric heating element in a 40-gallon water heater is rated at 5kW. You are planning on taking the hottest shower possible, and are therefore hoping your water heater is ready with all 40 gallons at 120ºF. Unfortunately, you realize your roommate has just gotten out of the shower and the temperature inside the water heater is now a measly 90ºF. How long will you have to wait before the water heater is back at 120ºF?It might help to know that the density of water is 3.79kg per gallon. – 35 minutesYou’re planning on making some hot water for tea. You need about 250 grams of water, and it comes out of the tap at 10ºC. You’re trying to decide whether you should use the microwave or your aluminum kettle (with a mass of 1kg). How much more energy would it take to heat up the water in the kettle, assuming that the aluminum of the kettle also starts at 10ºC? If the stove under the kettle and the microwave both were rated to output 1000W, how much longer would the kettle take to boil the water than the microwave? – 81 seconds