Since in COACH, these problems were assumed to be given after potential energy was taught, they will require either this concept, or energy input/output due to gravitational force which relates height change to Ein or Eout. I plan to talk about these idea on Friday, 13th. (or you can read sections 7.2 and 7.9, which are also required to do predictions and WUQs for the next week’s lab. Briefly, gravitation is capable of speeding up falling objects and slowing down objects going up in height. The speed change implies that kinetic energy of the object also increase or decrease. It turns out that the amount of kinetic energy given to or taken away from a falling/rising object only depends on how much the height changes, ∆ℎ, and given by 𝐸!" = 𝑚𝑔∆ℎ for a falling object, and 𝐸!"# = 𝑚𝑔∆ℎ, where in both cases, ∆ℎ is defined to be a positive quantity (falling distance or rising distance). Alternatively, since objects at large height is capable of becoming a fast moving object by falling, we have created an idea of “potential” energy, which is defined to be 𝑈 = 𝑚𝑔ℎ, where ℎ is the height and measured from some reference height (which can be defined in many ways just like coordinate origin can often be chosen in many ways. In this approach, falling object start with large potential energy, and as it falls, the potential energy gets smaller. It turns out that the sum of this potential energy and kinetic energy stays constant through the falling process. Namely, 𝐾! + 𝑈! = 𝐾! + 𝑈! . Either of these version of energy conservation (expansion from the previous version) is more useful than the previous kinetic energy only version. So here are two problems you can do using these ideas. If you are solving these problems with COACH, since it’s assuming that you have studied forces, there will be some questions involving forces, even though it’s not necessary to solve these problems. Know that neither problem involves friction, nor is there such force called “force of motion”. Normal force should be perpendicular to the surface that the object sits, and you have a pretty good idea which direction the gravity will point to. If you get stuck in COACH because a question involves unfamiliar concepts, please let me know by Email. E1. Emergency ramp (1) While driving in the mountains, you notice that when the freeway goes steeply downhill, there are emergency exits every few miles. These emergency exits are straight dirt ramps about 100 yards long that leave the freeway and are sloped uphill. They are designed to stop trucks and cars that lose their brakes on the downhill stretches of the freeway. You decide to figure out at what angle from the horizontal an emergency exit ramp should rise in order to stop a 50 metric ton truck going 70 mph, even if the road is covered with ice. P6. Skateboard (2) You are helping your friend prepare for the next skateboard exhibition by determining if the planned program will work. Your friend will take a running start and then jump onto a heavy-‐duty 15-‐lb stationary skateboard. The skateboard will glide in a straight line along a short, level section of track, then up a sloped concrete wall. The goal is to reach a height of at least 10 feet above the starting point before coming back down the slope. Your friend's maximum running speed to safely jump on the skateboard is 23 feet/second. Your friend weighs 150 lbs.