Gravitational Potential Energy and Total Energy

In Wednesday's class, we did not really do anything but answer the questions from page 290 #1-4 for the whole class.

In Thursday's class, we started the class by reading the pages 291-292 in our textbook about Potential Energy and Law of Conservation of Energy. After that, we then proceed and read through our notes about Gravitational Potential Energy and Total Energy.

Gravitational Potential Energy (Eg) is the energy that is stored when an object is placed in a vertical  position relative to the ground level (which is the surface of the earth or the floor of any room), or any base level.

The formula you can use to find the Eg of an object is:

Eg = mgh

where:

Eg = Gravitational Potential Energy (Joules or J)

m = the mass of an object (kg)

g = acceleration due to gravity (9.8 m/s^2)

h = change in height relative to the reference point (m)

*** There are other types of potential energy but in this class, when potential energy is mentioned, only gravitational potential energy is usually used.

Ex. A hydraulic hoist lifts a 1100 kg car 2.5 m. What is Eg?

m = 1100 kg 

h = 2.5 m

g = 9.8 m/s^2

Eg = ?

Eg = mgh

Eg = (1100kg)(9.8m/s^2)(2.5m)

Eg = 27000 J

After talking about gravitational potential energy, we also talked about Total Energy. 

In an object, there will be an equivalent increase in gravitational potential when work is being done. When an object is raised, potential and kinetic energy interchanged which means when one of the energy would increase, the other one would decrease. The sum of kinetic and gravitational potential energy remains constant in any system, and the total value of energy remain constant (Law of Conservation of Energy).

Etotal = Epotential + Ekinetic

Note **** Friction and Air Resistance are ignored in Conservation of Energy.

Examples:

1. Roller Coasters

- There would be most potential energy or gravitational energy at the highest point of a roller coaster (and there is zero kinetic energy) 

- At the lowest point, kinetic energy is when it has its maximum value (or zero potential energy)

2. Pendulums

- The distance from equilibrium is like the height above earth.

3. Springs

- There are more Elastic Potential Energy a spring has when it is further deformed. 

- The formula you can use to find elastic potential is: 

Ep(elastic) = 1/2kx^2

k = the spring constant (every spring has a specific k value)

x = how far from the equilibrium the spring is depressed or stretched (also called Hooke's Law)

Ex. A compressed spring that obeys Hooke's Law as a potential energy of 18 J. If the spring constant of the spring is 400 N/m, find the distance by which the spring is compressed. 

Ep = 18 J

k = 400 N/m

x = ?

Ep = 1/2kx^2

(2Ep)/k = x^2

(2(18J)) / 400 = x^2

36/400 = x^2

x = 0.30m