Conservation of Energy

Law of Conservation of energy states that in a closed, isolated system, energy can neither be created nor destroyed; rather, energy is conserved.

a. abbreviated version:KEi + PEi = KEf + PEf
                                         
b. extended version: 1/2mv^2i + mghi = 1/2mv^2f + mghf

a:The SI units is measured in joules (J)
b:The American Units is measured in calories.

6.) Tony Hawk (m = 66kg) rides his skateboard at a local skate park. He starts from the rest at the top of the track and begins a descent down the track, always maintaining contact with the surface. The mass of the skateboard is negligible, as is friction except where noted. What is hawk's speed when he reaches the bottom of the initial dip , 18.0 m below the starting point? 

mgh1 = mv^2/2 

v1 = √2gh1 = √ 2 * 9.81 * 18 = 18.8 m/s 

mgh1 = mv^2/ 2 + mgh2

mg(h1 - h2) = mv^2/2 

v2 = √2g(h1-h2) = √2* 9.81(18-10) = 12.5 m/s

v1= 18.8 m/s     v2= 12.5 m/s 

 Jeremy, 30 kg  is at the top of a 15 m ramp. He goes down the ramp. How fast is he going at the bottom of the ramp ? 

Ki + PEi = Kf + PEf 

MVi^2 / 2+ MGHi = MVf^2 / 2 + MGHf  

(30kg)(0m/s)^2 + (30kg)(-9.8m/s^2)(15m)= (30kg)Vf^2 + (30kg)(-9.8m/s^2)(-15m)

Vf= 

 Known

Vi= 0 m/s.      

M= 30 kg
Hi= 15 m
Hf= -15

When the skater is at the top of the loop the potential energy is at its highest. 

The kinetic energy is turning back to the potential energy that will later lead back. 

When the skater is at the top of the ramp, there is absolutely no kinetic energy. The potential energy and total energy increased. 

At the end of the ramp, the skaters kinetic energy increases. But there is absolutely no potential energy.