Name ______________________________ Unit 7: Worksheet 5 Conversion Factors: 1 Calorie = 4180J 1hp = 746W or J/s 1kW·hr = 3,600,000J 1. Two British engineers developed a product called the GravityLight, a safe alternative to using kerosene lamps commonly used in developing nations. The smoke inhaled from kerosene lamps is equivalent to smoking 2 packs of cigarettes every day which can cause lung cancer. Lifting the 9kg mass to a height of 1.2m provides enough energy to power an LED light bulb for a short time. a. How much gravitational energy is stored by lifting the mass to height of 1.2m? b. If the LED bulb uses energy at rate of 0.1W or J/s, how much time will the light stay on with initial gravitational energy found in part (a)? If interested check out the website for more information on the GravityLight: http://www.indiegogo.com/projects/gravitylight-lighting-for-developing-countries 2. How many joules of electrical energy does your 1600W blow drier use if you dry your hair for 5.0 min? 3. Your electric utility company sends you a monthly bill informing you of the number of kilowatt- hours you have used that month. Hint: 1kW·hr = 1000W·3600s = 3,600,000J Is the utility charging you for energy or power? Explain. 4. If a refrigerator uses on average 500 kilowatt-hours of energy each year what is its average power rating measured in Watts (how many joules of energy does it uses each second)? (1kw*hr = 3.6x106J) 5. An 82 kg hiker climbs Pike’s Pike in Colorado. During a 6 hour period, the hiker's vertical elevation increases by 2,255 meters. 1 a. Calculate the climber's ∆Eg from the bottom to the top of the mountain. b. How many M&M’s would the hiker have to eat to replenish the energy lost hiking up the mountain? Each M&M contains 3.4 calories of stored chemical energy. Hint: 1st convert calories into Joules of energy for each M&M. c. Find the average power rating of the hiker used when hiking up the mountain. 6. An efficient LED light bulb uses energy at a rate of 7W or 7 J/s. What total amount of electrical energy is used if the light is on for 2 hours? 7. How much time would a student have to pedal the bicycle generator to store the needed amount of energy found in question 6, if the student is able to continuously produce 30W of power while pedaling? Unit 7 (Energy) Worksheet 5 Answer Key 1a. Eg = mgh = (9kg)(10N/kg)(1.2m) = 108J 2 b. P = ΔE/t, 0.1W = 108J/Δt, solving for Δt = (108J) / (0.1J/s) = 1,080s or 18min. 2. Solve for the change in energy using the power equation, and don’t forget to convert the given time of 5min into seconds (5min = 300s). P = ΔE/t, 1600W = ΔE / 300s, solving for ΔE = (1600J/s)*(300s) = 480,000J 3. The utility charges you for energy in kilowatt-hours. If you simplify kilowatt-hours you will get just units of joules which is the standard unit for energy. 4. The refrigerator uses, on average, 1.8 billion joules of energy each year which is 31,536,000s, or 57J of energy each second. so Paverage = 57J/s or W 5. a. Eg = mgh = (82kg)(10N/kg)(2,255m) = 1,849,100J b. Each M&M contains 3.4calories or 14,212J of energy, so she would have to eat, at minimum, 1,8949,100J / (14,212 J/M&M) or 130M&Ms to replenish the energy used to climb the mountain. c. P = ΔE/t = energy change / time = 1,849,100J / 21,600s = 61.6J/s or Watts 6. Solve for the change in energy using the power equation, and don’t forget to convert the given time of 2hr into seconds (2hr = 7200s). P = ΔE/t, 7W = ΔE / 7200s, solving for ΔE = (7J/s)*(7200s) = 50,400J 7. We know that we want the student to be able to generator 50,400J of energy, and the problem says they can continuously produce 30W of power which is 30J/s. Use the given information and the power equation to solve for the time (Δt): P = ΔE/t, 30J/s = 50,400J/Δt, solving for Δt = (50,400J) / (30J/s) = 1,680s or 28min. So it requires 28min of pedaling on the bicycle generator to store enough energy (50,400J) in a battery for the LED light to stay lit for 2 hours. 3
