1. Work and Energy

2. Potential Energy PE g = mgh Kinetic Energy KE = ½ mv 2 Work W = Fd

3. Conservation of Energy PE i + KE i = PE f + KE f mgh i + ½ mv i 2 = mgh f + ½ mv f 2 What happens if there is friction? Energy isn’t conserved. mgh i + ½ mv i 2 = W fric + mgh f + ½ mv f 2

4. Conservation of Energy mgh i + ½ mv i 2 = W fric + mgh f + ½ mv f 2 mgh i + ½ mv i 2 = W + mgh f + ½ mv f 2 What if work was defined as change in work? W = W i – W f (W i > W f ) mgh i + ½ mv i 2 = W i – W f + mgh f + ½ mv f 2 W i + mgh i + ½ mv i 2 = W f + mgh f + ½ mv f 2

5. Work and Energy W i + mgh i + ½ mv i 2 = W f + mgh f + ½ mv f 2 What about fluids though? Divide by volume? m/V = ρ

6. Energy Potential Energy PE g = mgh PE g /V= ρgh Kinetic Energy KE = ½ mv 2 KE/V = ½ ρv 2 Work W = Fd W/V = F/A P = F/A What are the units of pressure? J/m 3 = N/m 2 = Pa

7. Energy of Fluids W i + mgh i + ½ mv i 2 = W f + mgh f + ½ mv f 2 Divide by Volume! P i + ρgh i + ½ ρv i 2 = P f + ρgh f + ½ ρv f 2 This is called Bernoulli’s Equation This equation relates the conservation of mechanical energy to fluids.

8. Energy of Fluids P i + ρgh i + ½ ρv i 2 = P f + ρgh f + ½ ρv f 2 What does this equation mean? What happens to pressure when velocity increases and the height doesn’t change? (v f > v i ) P i + ½ ρv i 2 = P f + ½ ρv f 2 Answer: P i > P f What happens to pressure when the height decreases and the velocity doesn’t change? (h f < h i ) P i + ρgh i = P f + ρgh f Answer: P i > P f

9. 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, P i = 0 Pa Solution: P i + ρgh i + ½ ρv i 2 = P f + ρgh f + ½ ρv f 2 P i = v i = v f = h f = 0 0 + ρgh i + 0 = P f + 0 + 0 ρgh i = P f (1000)(9.81)(10) = 98,100 Pa (about 1 atm) (1000)(9.81)(20) = 196,200 Pa (about 2 atm)

10. https://www.youtube.com/watch?v=Na9ORhY jvJU https://www.youtube.com/watch?v=Na9ORhY jvJU

11. 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?