Work and Energy

Work and Energy

• Potential EnergyPEg = mgh

• Kinetic EnergyKE = ½ mv2

• WorkW = Fd

Conservation of Energy

• PEi + KEi = PEf + KEf

• mghi + ½ mvi2 = mghf + ½ mvf

2

What happens if there is friction?Energy isn’t conserved.

• mghi + ½ mvi2 = Wfric + mghf + ½ mvf

2

Conservation of Energy

• mghi + ½ mvi2 = Wfric + mghf + ½ mvf

2

• mghi + ½ mvi2 = W + mghf + ½ mvf

2

mghi + ½ mvi2 = W + mghf + ½ mvf

2

• What if work was defined as change in work?• W = Wi – Wf (Wi > Wf)

mghi + ½ mvi2 = Wi – Wf + mghf + ½ mvf

2

Wi + mghi + ½ mvi2 = Wf + mghf + ½ mvf

2

Work and Energy

• Wi + mghi + ½ mvi2 = Wf + mghf + ½ mvf

2

• What about fluids though? Divide by volume?

m/V = ρ

Energy• Potential Energy

PEg = mgh

PEg/V= ρgh

• Kinetic EnergyKE = ½ mv2

KE/V = ½ ρv2

• WorkW = FdW/V = F/AP = F/AWhat are the units of pressure?

J/m3 = N/m2 = Pa

Energy of Fluids

• Wi + mghi + ½ mvi2 = Wf + mghf + ½ mvf

2

• Divide by Volume!

• Pi + ρghi + ½ ρvi2 = Pf + ρghf + ½ ρvf

2

• This is called Bernoulli’s EquationThis equation relates the conservation of mechanical

energy to fluids.

Energy of Fluids• Pi + ρghi + ½ ρvi

2 = Pf + ρghf + ½ ρvf2

• What does this equation mean?

• What happens to pressure when velocity increases and the height doesn’t change? (vf > vi)

• Pi + ½ ρvi2 = Pf + ½ ρvf

2

• Answer: Pi > Pf

• What happens to pressure when the height decreases and the velocity doesn’t change? (hf < hi)

• Pi + ρghi = Pf + ρghf

• Answer: Pi > Pf

Problem

• A-Aron wants to go scuba diving in still (not moving) oceanwater at a depth of 10m. What pressure would he feel at that depth? What about 20m?Hint: What is the velocity? ρ = 1000 kg/m^3, Pi = 0 Pa

• Solution:Pi + ρghi + ½ ρvi

2 = Pf + ρghf + ½ ρvf2

Pi = vi = vf = hf = 0

0 + ρghi + 0 = Pf + 0 + 0

ρghi = Pf

(1000)(9.81)(10) = 98,100 Pa (about 1 atm) (1000)(9.81)(20) = 196,200 Pa (about 2 atm)

• https://www.youtube.com/watch?v=Na9ORhYjvJU

Carbon Sequestration

• Carbon sequestration is the capture and storage of CO2 created during industrial processes such as in power plants. It is also one of the grand challenges.

• People are looking into possibly storing it in old oil and gas fields. Since those won’t have enough room, rock formations 800m deep or even the ocean floor, which can be 2 or more km down, are possibilities.

• What pressure would be experienced 2 km deep in the ocean?