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### Energy Conservation Conceptually Determine whether each of the scenarios below violates energy conservation. Explain your answers. Also, note that some of these might be impossible for reasons other than energy conservation. 1. On a perfectly flat surface (with friction so he can move, but no...

### Energy Conservation Conceptually Determine whether each of the scenarios below violates energy conservation. Explain your answers. Also, note that some of these might be impossible for reasons other than energy conservation. 1. On a perfectly flat surface (with friction so he can move, but no air resistance), a runner "burns calories" by running in a perfectly straight line with a perfectly constant speed. * Yes it does violate energy conservation because when she burns calories, it turns into heat, which transfers to the atmosphere. 2. 2 perfectly rigid objects traveling in opposite directions crash into each other. The collision produces no sound, heat, or permanent changes to the objects. As a result of the collision, both objects come to a stop. * Yes it does because kinetic energy is lost to somewhere and that energy has to be transferred to thermal energy ### Rotation 1. Some experimental types of hybrid cars use a mechanical flywheel to store energy that is then given back to the car. Flywheels are typically made of steel disks that have a radius of about 1/2 meters and a mass of about 30 kg. How fast would the disk need to spin to be able to accelerate a 1000 kg car to 5 meters per second? * **Kinetic energy** = (1/2) * *mv*2 = (1/2) * 1000 * 52 = 12500 J * **Rotational kinetic energy** = (1/2) * I * ω2 * 12500 = (1/2) * 3.75 * ω2 * ω2 = 6666.67 * ω = 81.65 rad/s 2. A car with mass *M* (not including the wheels) has 4 wheels each of mass *m* that are solid cylinders. If the car is released from a height *h* on a ramp, what will be the speed of the car when it reaches the bottom? * **Ei** = **Ef** * **2*m*g*h* = **(1/2)*M*v*2 + 4 * (1/2)*m*v*2 * **2*m*g*h* = (1/2) * v2 * (M + 4*m) * **2*g*h* = (1/2) * v2 * **8*g*h* = v2 * **v = √(8*g*h)**