Law of Conservation of Energy
The law of Conservation of Energy states that the total energy of an isolated system remains constant, it is said to be conserved over time.
Eᵢ = Eꝼ
Kᵢ + Pᵢ = Kꝼ + Pꝼ
mvᵢ² + mghᵢ = mvꝼ² + mghꝼ
2 2
SI Units
1 Joule = 1 kg
m
sAmerican Units
1 Joule (J) is the MKS unit of energy
In the video we can see how energy is conserved.In the universe as a whole, energy is never destroyed -- it just changes forms. When a rock falls, for example, the gravitational potential it possessed by virtue of its height is turned into kinetic energy, and when it strikes the ground that kinetic energy turns into heat. Plants take radiation and convert the energy it contains into chemical potential energy that you in turn extract when you eat your food. A power plant takes chemical potential energy in coal and turns it into electrical energy. In all of these scenarios, energy is just changing forms.
Problem 1
rides his skateboard at a local skate park. He starts from rest at the top of the track as seen in the figure below 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.
(a) What is Shawn’s speed when he reaches the bottom of the initial dip, 18.0 m below the starting point?
(b) He then ascends the other side of the dip to the top of a hill, 8.0 m above the ground. What is his speed when he reaches this point?
Solution:
Known variables
m = 66 kg
Vᵢ = 0 m/s
h = 18 m
h₂ = 8 m
Unknown variables
V₁= ?
v₂ = ?
a. From the conservation of energy: Potential energy at the top of the 18 m transforms into the Kinetic energy at the bottom of the dip.
b. From the conservation of energy: Potential energy at the top of the 18 m transforms into the Kinetic and Potential energy at the top of a hill.
Answer:
and 
Problem 2
An intrepid physics student decides to try bungee jumping. She obtains a cord that is
m long and has a spring constant of 
. When fully suited, she has a mass of 
. She looks for a bridge to which she can tie the cord and step off. Determine the minimum height of the bridge L, that will allow her to stay dry (that is, so that she stops just before hitting the water below). Assume air resistance that is negligible.
Solution:
From the conservation of energy, we have kinetic and elastic energies that have transformed into potential energy:
Where
Therefore
We have two solutions:
and 
The height of the bridge can’t be less than length of cord, therefore we select only
m.Answer:
m.
Energy is distributed