Potential Energy E p = mgh mass gravity height double if you double the mass then the PE will 10 m/s 2 the value for gravity is double if you double the height then the PE will Where is the Potential energy the least in the picture below? The PE is the least at the lowest point (the bottom part of the swinging motion). Identify two ways you could increase the potential energy. 1. increase mass 2. increase height 1 Page
Create three illustrations of an object(s) that has potential energy. Identify the mass and height of each object. Then, rank each of your illustrations from greatest to least. Knowing that the potential energy at the top of the tall platform is 50 J, what is the potential energy at the other positions shown on the stair steps and the incline? 2 Page
Kinetic Energy mass velocity if you double the mass then the KE will if you double the velocity then the KE will double quadruple E k = ½ mv 2 Symbols: E k means kinetic energy Units: Joules m means mass Units: kg v 2 means velocity 2 Units: m/s If I want to find: Then I need to know: My formula will be: Mass & velocity ½ mv 2 Joules My unit will be: Mass Velocity & kinetic energy m=2e k /v 2 kg Velocity Mass & kinetic energy v= 2E k /m m/s 3 Page
Which of the following statements are true about kinetic energy? Include all that apply. 1. is the form of mechanical energy which depends upon the position of an object. 2. If an object is at rest, then it does not have any kinetic energy. 3. If an object is on the ground, then it does not have any kinetic energy. 4. The kinetic energy of an object is dependent upon the mass and the speed of an object. 5. Faster moving objects always have a greater kinetic energy. 6. More massive objects always have a greater kinetic energy. 7. An object has a kinetic energy of 40 J. If its mass were twice as much, then its kinetic energy would be 80 J. 8. An object has a kinetic energy of 40 J. If its speed were twice as much, then its kinetic energy would be 80 J. 9. Object A has a mass of 1 kg and a speed of 2 m/s. Object B has a mass of 2 kg and a speed of 1 m/s. Objects A and B have the same kinetic energy. Rank these four objects in increasing order of kinetic energy, beginning with the smallest. Object A m = 5.0 kg v = 4.0 m/s h = 2.0 m Object B Object C Object D m = 10.0 kg v = 2.0 m/s h = 3.00 m m = 1.0 kg v = 5.0 m/s h = 5.0 m m = 5.0 kg v = 2.0 m/s h = 4.0 m Answer: D < C < B < A Examples 1. Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s. (105000 Joules) Kinetic Energy m=625 kg v=18.3 m/s 105000 Joules 2. If the roller coaster car in the above problem were moving with twice the speed, then what would be its new kinetic energy? (419000 Joules) Kinetic Energy m=625 kg v=36.6 m/s 419000 Joules 3. Missy Diwater, the former platform diver for the Ringling Brother's Circus, had a kinetic energy of 12 000 J just prior to hitting the bucket of water. If Missy's mass is 40 kg, then what is her speed? (24.5 m/s) 24.5 m/s velocity KE=12000 J m=40 kg 4 Page
Which of the following statements are true about potential energy? Include all that apply. 1. Moving objects cannot have potential energy. 2. Potential energy is the energy stored in an object due to its position. 3. Potential energy is dependent upon the mass of an object. 4. If the mass of an elevated object is doubled, then its gravitational potential energy will be doubled as well. 5. Gravitational potential energy is lost as objects free-fall to the ground. 6. The higher that an object is, the more potential energy which it will have. 7. The unit of measurement for potential energy is the Joule. 8. A 1-kg mass at a height of 1 meter has a potential energy of 1 Joule. Rank these four objects in increasing order of potential energy, beginning with the smallest. Object A m = 5.0 kg v = 4.0 m/s h = 2.0 m Object B Object C Object D m = 10.0 kg v = 2.0 m/s h = 3.00 m m = 1.0 kg v = 5.0 m/s h = 5.0 m m = 5.0 kg v = 2.0 m/s h = 4.0 m Answer: C < A < D < B Examples 1. A platform diver has a mass of 50 kg. She steps off a diving board that is elevated to a height of 10 meters above the water. Calculate her potential energy. Potential Energy m=50 kg h=10 m g = 10 m/s 2 PE=mgh 5000 Joules 2. Theresa s 5.45 kg dog, Mr. Muggles is napping on top of 2 meter high couch. What is the potential energy of Mr. Muggles? Potential Energy m=5.45 kg h=2 m g = 10 m/s 2 PE=mgh 109 Joules 5 Page
Class Work 1. Garfield (mass = 10.5 kg) is sleeping on top of the 3 meter high couch. What is Garfield s potential energy? Potential energy m=10.5 kg h=3 m g=10 m/s 2 PE=mgh 315 Joules 2. A 200 kg pig is standing on top of a 40 meter high muddy hill. What is the pig s potential energy? Potential energy m=200 kg h=40m g=10 m/s 2 PE=mgh 80000 Joules 3. Tyler (mass=50-kg) is riding in a go-kart down maple avenue. a. What is Tyler s kinetic energy if he travels at 2 m/s? m=50 kg 100 Joules v= 2m/s b. What is Tyler s kinetic energy if he travels at 4 m/s? m=50 kg v= 4m/s 400 Joules 6 Page
Group Work 1. Alan, a hot dog vendor, is selling hot dogs on top of a hill (height = 20 m) outside of Petco Park in San Diego California. While talking to a customer, Alan s hot dog cart starts to roll down the hill. a. What is the kinetic energy of the cart as it rolls down the hill with a velocity of 3.25 m/s? m=35 kg 184.84 Joules v= 3.25m/s b. What is the potential energy at the top of the hill? Potential energy m=35 kg h=20m g=10 m/s 2 PE=mgh 7000 Joules mass = 35 kg 2. True or False: If the speed of an object doubles, the kinetic energy of the object doubles. 3. If the kinetic energy of a 625-kg roller coaster car is 105000 Joules: a. Determine how fast it moves. Velocity m=625 kg Ek = 105000 J v= 2E k /m 57.97 m/s b. If the velocity of the coaster were to double what would its new Kinetic Energy be? m=625 kg 4200000 J v= 115.94 m/s 4. Mister Diwater, the former platform diver for the Ringling Brother's Circus, had a kinetic energy of 14000 J just prior to hitting the bucket of water. If Mister s mass is 70 kg, then what is his speed? Velocity m=70 kg 20 m/s Ek = 14000 J v= 2E k /m 7 Page
HomeWork 1. In 1987, the fastest auto race in the United States was the Busch Clash in Daytona, Florida. That year, the winner s average speed was about 88 m/s. Suppose the kinetic energy of the winning car was 3,800,000 J. What was the mass of the car and its driver? Mass v=88 m/s 981 kg Ek=3,800,000 J m=2e k /v 2 2. In 1994, Leroy Burrell of the United States set what was then a new world record for the men s 100 m run. He ran the 100 m distance with an average speed of 10.2 m/s. Assuming that he ran with constant speed, and his mass was 65-kg, what was Burrell s kinetic energy? m=65 kg v= 10.2 m/s 3381.3 J 3. The fastest helicopter, the Westland Lynx, has a top speed of 111 m/s. If its mass was 3400 kg, what is the helicopter s kinetic energy? m=3400 kg v= 111 m/s 20945700 J 4. Dan Jansen of the United States won a speed-skating competition at the 1994 Winter Olympics in Lillehammer, Norway. He did this by skating 500 m with an average speed of 14 m/s. If his kinetic energy was 6540 J, what was his mass? Mass v=14 m/s 66.73 kg Ek=6540 J m=2e k /v 2 5. Charlie s mass is 101.0 kg, and as he ski s down the slopes his kinetic energy is 99,600 J. What speed does Charlie travel down the slopes? Velocity m=101 kg Ek = 99,600 J v= 2E k /m 44.41 m/s 6. Susie Maroney from Australia set a women s record in long-distance swimming by swimming 93,625 m in 24.00 h. What was Maroney s average speed (in m/s)? If Maroney s mass was 55 kg, what was her kinetic energy? m=3400 kg v= 111 m/s 20945700 J 7. Does doubling the mass OR doubling the speed have the most effect on kinetic energy? Doubling the speed. 8 Page
Sample Problems 1. A 2 kg car moving with a speed of 2 m/sec starts up a hill. How high does the car roll before it stops? What type of energy does the car have when it is on the ground traveling at 2 m/s? Kinetic Energy Calculate this energy: KE M=2 kg V=2 m/s 4 Joules If the car is at rest at the top of the ramp, then what type of energy does the car have? Potential Energy If energy is conserved, what is the value of the energy the car has at the top of the ramp? 4 Joules Use this information; determine how high the car is. height KE= 4 Joules KE=PE KE=mgh 0.2 meters 2. A 10-kg roller coaster has a velocity of 25 m/s at the bottom of the first hill it travels down. How high was the hill? What type of energy does the car have when it is at the bottom of the first hill traveling at 25 m/s? Kinetic Energy Calculate this energy: KE M=10-kg V=25 m/s 3125 Joules If the car is at rest at the top of the hill, then what type of energy does the car have? Potential Energy If energy is conserved, what is the value of the energy the car has at the top of the hill? 3125 Joules Use this information; determine the height of the hill. height KE=3125 Joules KE=PE KE=mgh 31.25 meters 9 Page
Class Work 3. A 500-kg children s roller coaster is released from the top of a track(vi=0). If its maximum speed at ground level (hf=0) is 8 m/s, find the height it was released from. What type of energy does the roller coaster have at ground level? Kinetic Energy Calculate this energy: KE M=500 kg V= 8 m/s 16000 Joules If the roller coaster is at rest at the top of the track, then what type of energy does the car have? Potential Energy If energy is conserved, what is the value of the energy the roller coaster has at the top of the hill? 16000 Joules Use this information; determine the height of the track. height KE=16000 Joules KE=PE KE=mgh 3.2 meters 4. A 2-kg rock is dropped (vi=0) from a height of 2.7 m. How fast is it going when it hits the ground (hf=0)? What type of energy does the rock have at a height of 2.7 meters? Potential Energy Calculate this energy: PE M=2 kg H=2.7 m PE=mgh 54 Joules If the rock hits the ground, what type of energy does it have? Kinetic Energy If energy is conserved, what is the value of the energy of the rock as it strikes the ground? 54 Joules 10 Page
5. Calculate the potential energy, kinetic energy, mechanical energy, velocity, and height of the skater at the various locations. 6. A 0.750-kg ball will rise if it is kicked straight up with an initial speed of 17.0 meters per second. a) Calculate the kinetic energy of the ball immediately after it is kicked. KE M=0.75 kg V=17 m/s 108.375 Joules b) What is the potential energy of the ball at its maximum height? PE KE=108.375 Joules KE=PE 108.375 Joules c) What is the maximum height the ball will rise? Height KE=108.375 Joules KE=PE KE=mgh 14.45 meters 11 Page