Tree Bridges & Energy

This is a picture of my friend Sarah and I standing on a fallen tree that we found when we were hiking in Nuuanu. The tree was about fifteen feet off the ground and knowing this information would could have calculated our potential energy by using the equation PE = mv. Our potential energy while standing on top of the tree equals our kinetic energy at the ground if we had fallen off. So we could have figured out the velocity we would have been moving at when we hit the ground at if we had fallen by using the equation PE = KE, mv =(1/2)(m)(v)(v). Knowing our velocity at ground level, we could use the momentum formula, P = mv, to figure out what our momentum would be at the bottom of the fall. Impulse (J) is a force that acts for a certain amount of time and it represents change in momentum, J = (F)(t)= change in P= mv. So we know that the impulse exerted on us when we hit the ground is equal to mv. Luckily, we both have sick balancing skills and neither of us fell, which considering that the impulse would be rather large would have hurt a lot, but it is interesting to know that you can basically calculate how much a fall will hurt with only a very small amount of starting information (mass and height). 

Brothers & Energy

A couple summers ago, my brothers, their friends, and I went out to the Mokolua Islands in Lanikai and jumped off the rocks at Shark's Cove. In this picture, my brother Ian is in the air and my brother Haakon is standing up on the rocks waiting to jump. Ian has both potential and kinetic energy. Ian's potential energy is with respect to the water, as soon as he jumped off the rock, his potential energy started to transfer to kinetic energy, and as he gets closer to the water his potential energy will get smaller and smaller. Potential energy can be negative or positive, depending of the reference level, and because my reference level is the water, Ian will have negative potential energy once he hits the water and goes under. The equation for potential energy is PE=mgh. Haakon is not in motion, so his velocity is zero, so his kinetic energy is zero, because KE=1/2mv2. All of Haakon's energy is potential. However, once Haakon jumps off the rock his potential energy will begin to transfer to kinetic energy, just as Ian's did. In a closed system, total energy is always constant and TE=PE + KE. PE can be negative or positive, depending on your reference point, but KE is always positive. An object only has KE if it is in motion.