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## Potential and Kinetic Energy

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**Work Review**• Work is done when a force is exerted over a distance • Which is work? • When you drive into a wall and smash your fender • A man walking at a steady pace carrying a briefcase • When you spend an hour in a futile effort to move a large boulder • Why? • W = F X d • 1 joule of Work=1 newton of Force X 1 meter of Distance**Challenge**• A 50-Pound crate is pushed across the floor by a 20-pound horizontal force. Aside from the pushing force and gravity, there is also a 50-pound force exerted upward on the crate and a 10-pound frictional force. • Construct a free body diagram • Which of these forces does no work? • Which does positive work? • Which does negative work?**Types of Potential Energy:**Elastic Potential Energy – a stretched or compressed spring or rubber band. A bow drawn back. 2. Gravitational Potential Energy – the energy stored in an object as the result of its vertical position or height.**Gravitational Potential Energy (GPE)**There is a DIRECT relationship between GPE and the mass of an object. What does that mean? There is a direct relation between GPE and the height of an object. The mass (m) of the object times the acceleration of gravity (g) is the same as the weight of the object in newtons. • Pegrav = mass x g x height • m= mass of an object • h= height of an object • g= gravitational field strength (9.8 N/kg on Earth) • Mass of an object in kg X 9.8 m/s2 = weight of the object in newtons.**Challenge problem:**• The principle from the slide before to determine the blanks in the following diagram. • Given: the potential energy at the top of the platform is 50 J. • Question: What is the potential energy at the other positions shown?**Answers:**• A: PE = 40 J (since the same mass is elevated to 4/5-ths height of the top stair) • B: PE = 30 J (since the same mass is elevated to 3/5-ths height of the top stair) • C: PE = 20 J (since the same mass is elevated to 2/5-ths height of the top stair) • D: PE = 10 J (since the same mass is elevated to 1/5-ths height of the top stair) • E and F: PE = 0 J (since the same mass is at the same zero height position as shown for the bottom stair).**Kinetic Energy**• The energy of motion • Two Factors govern the amount of K energy in an object • Kinetic energy is proportional to mass • If you double the mass, you double the kinetic energy • Kinetic energy increases as the square of its velocity • If you double the speed, you increase the kinetic energy 4 times • Mathematically, kinetic energy equals the mass of the moving object times the square of that objects velocity, multiplied by the constant ½ • KE (in joules) = ½ X mass (in kg) X (velocity2) • KE = ½ mv²**Sample problem:**A 50 kg boy and his 100 kg father went jogging. Both ran at a rate of 5 m/s. Who had more kinetic energy? • Solution: Although the boy and his father were running at the same speed, the father has more kinetic energy because he has more mass. 1. The kinetic energy of the boy: 2. The kinetic energy of the father:**Solution:**Boy KE = (50/2) (52) = 25 x 25 = 625 J Dad KE =KE = 1/2mv2 (100/2)(25)= (50)(25)= 1250 J**What is the potential energy of a 10 N book that is placed**on a shelf that is 2.5 m high? Solution: The book’s weight (10 N) is equal to its mass times the acceleration of gravity. Therefore, you can easily use this value in the potential energy formula: PE = mgh PE = 10 x 9.8 x 2.5 = 245 J**Solution:**• PE = 10 x 9.8 x 2.5 = 245 J