Energy Transfer. Examples of lots of Kinetic Energy What about this one. So what does K depend on? Kinetic Energy depends not only on the speed, but also the mass of the object. K = mv 2 Increasing velocity has a greater effect than increasing mass Proportional Reasoning What would happen to the kinetic energy of an object if I. Doubled the mass? Quadrupled the mass? Cut the mass by 1/3? Proportional Reasoning What would happen to the kinetic energy of an object if I. Doubled the velocity? Quadrupled the velocity? Cut the velocity by 1/3? 4x Calculations Usain Bolt has a mass of 94 kg and can reach a speed of 12.2 m/s. Calculate his K. At 31 m/s, the cheetah has 28,830 J of kinetic energy. Calculate his mass. T-Rex has a mass of 6,000 kg and has 192,000 J of kinetic energy. Calculate his velocity. Show car video Show sliding car Now its time for calculations Here is a graph of v vs. t. What is the cars initial velocity? What is the cars final velocity? Mass of the prius is roughly 2,000 kg Calculate the change in kinetic energy Draw Free Body Diagram for the car after applying the brakes What direction is the car moving? What direction is friction? What does this tell you about the work being done on the car? Calculating Work W = F x d Force Only force doing work is friction, and Newtons 2 nd Law states that F = ma. W = (ma) x d We know the mass of the prius, but what about its acceleration? Looking back. How did we find acceleration from a v vs. t graph? Calculating Work We had the equation, W = (ma) x d We now know m and a What about the distance travelled? How can we get it from the v vs. t graph? Area.but that isnt a pretty shape. x vs. t graph is WAY easier Calculating Work Were still doing this?!? Calculating Work W = (ma) x d W = 2000 kg x m/s/s x m W = -32, J But wait We said the change in kinetic energy was -32,670 J And the work done by friction was equal to -32,707 J. Thats because. W = K Work-Energy Theorem