9-1-2 GravPotentialEnergyAssignment

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Jan 9, 2024

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Gravitational potential energy Potential energy is a form of energy that comes from an object’s position. Gravitational potential energy comes from an object’s height in the presence of gravity. Hand-held objects at heights of one or two meters have potential energies between 1 and 100 joules. A 6,000 kg helicopter at an altitude of 1,000 m (1 km) has a potential energy of 60 million joules. Gravitational potential energy depends linearly on height and mass. For example, increasing the height tenfold will increase the potential energy by a factor of ten. Note that the value of g remains constant for all objects near Earth’s surface. Typical potential energies of everyday objects at typical heights (on/near Earth’s surface): mass (kg) height (m) g (N/kg) E P (J) baseball 0.15 1 9.8 1.47 baseball 0.15 10 9.8 14.7 arrow 0.01 100 9.8 9.8 seagull 1.75 50 9.8 857 diver 50 10 9.8 4,900 helicopter 6,000 1,000 9.8 58,800,000 Applying new knowledge When calculating the potential energy in problems 1 – 6 below, compare your final answers to the typical values shown in the table to see if they make sense. Example: Calculate the potential energy of a 3.0 kg rock at a height of 15 m. 1. Calculate the potential energy of a 5.0 g (0.005 kg) paper airplane 5.0 meters above the ground. 0.005*10*5=0.25J 2. Calculate the potential energy of a 6.3 kg eagle flying at a height of 75 m. 6.3*10*75=4725J E p = mgh = (3.0 kg)(9.8 N/kg)(15 m) = 441 J E p = mgh 1

3. Calculate the potential energy of a 40 gram sparrow resting on a branch 30 feet above the ground. (Hint: 1 foot = 0.305 m) 0.04*10*9.15=3.66J 4. How much potential energy is required to lift a 50 gram arrow to a height of 100 meters? 0.05*10*100=50J 5. Which has more potential energy: a 1.0 kg ball at a height of 10 m, or a 10 kg ball at a height of 1.0 m? 1*10*10=100J 10*10*1=100J They are the same amount of PE. 6. What is the height of a 2.00 kg object if its potential energy is 100 J? 2*10*h=100 10*h=50 H=5 5m 7. A 2.5 kg falcon soaring at a height of 500 meters has a certain potential energy. Now suppose the falcon were carrying a 1.0 kg snake. What would the new height be if the total potential energy were to remain the same? 2.5*10*500=12500J 3.5*10*h=12500 10*h=3571 H=357.1 2

8. Calculate the potential energy of a small plane that weighs 7,200 pounds and is traveling at a speed of 80 mph at an altitude of 5,500 feet. (Hint: 1 foot = 0.30 m and 1 kg weighs 2.2 lbs. on or near Earth’s surface) 3273*10 3

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