1. Conservation of Energy and Power
St. Augustine Preparatory School
October 18, 2016

2. Mechanical Energy
Mechanical Energy: the sum of kinetic energy and all forms of potential energy. In a frictionless situation, mechanical energy is conserved. Example: If an object has 10 J of potential energy while sitting on a table, then just as it hits the ground, it will have 10 J of kinetic energy. In a situation with friction some mechanical energy is lost as heat.

3. Conservation of Mechanical Energy
Previously we said that mechanical energy is conserved. ex. If an object has 10 J of potential energy while sitting on a table, then just as it hits the ground, it will have 10 J of kinetic energy.

5. Friction
Friction is present whenever two physical surfaces are in contact
When one object slides on another object, some of the kinetic energy present will be lost in the form of heat
The heat given off is a non-mechanical form of energy, meaning that mechanical energy is rarely 100% conserved in day-to-day processes

6. Note:
The total energy is conserved, but the mechanical energy is not conserved
Example:
10 J of EP = 9 J of Ek + 1 J of heat
The energy at the beginning is still there at the end, however, our mechanical energy (Ep and Ek) is 1 J less after the movement took place

7. Practice Problems Page 172: 1, 2, 3 Page 171: 5 Page 161: 22, 21
Answers:
2.93 m/s2 m m
x102m or 20.m

8. Power

9. Which movie is this from?
“I live my life a quarter mile at a time. Nothing else matters: not the mortgage, not the store, not my team and all their bulls***. For those ten seconds or less, I'm free.”

10. What is Power?
Power is the rate at which work is done. It can also be thought of as the rate at which energy can be transferred.
If you think of a car that has a lot of power, it converts energy from the gasoline to kinetic energy very quickly.
Lots of power does not guarantee high speed though. Power to weight ratio is very important.

11. Carbon Fiber reduces weight on performance cars

12. Unit of Power The unit for power that we will be using is the Watt (W)
A popular unit of power that you have likely heard of before is horsepower
What is horsepower and where did it come from?
Youtube Video

13. Two Formulas for Power:
Power (J) = work (Nm) divided by time (s)
P = Fv
Power (J) = Force (N) multiplied by velocity (m/s)

14. Practice Problem 1
1) An interior decorator is installing a large curtain in an acting theatre. The curtain has a mass of 193 kg and will have to be raised 7.5 m in a time of 5.0 seconds. The interior decorator has access to three different motors with different power ratings: 1.0 kW, 3.5 kW, 5.5 kW. Which motor is best for the job?

15. Solution
P = W/t The work done will be to overcome gravity, so we must find the force of gravity: Fg = mg = (193kg)(9.81m/s2) = N W = Fd = ( N)(7.5m) = Nm P = W/t = Nm / 5.0 s = W W = 2.8 kW The 3.5 kW motor should be used.

16. Practice Problem 2
A tow truck uses a W electric winch to pull a car out of the ditch. If the car travels meters in 45.0 seconds, what force was applied to the car?

17. Solution
A tow truck uses a W electric winch to pull a car out of the ditch. If the car travels meters in 45.0 seconds, what force was applied to the car?
P = Fv
P = F(Δx/Δt)
1500W = F(25m/45.0s)
1500 W = F(0.555…m/s)
2700 N = F