1. Work, energy, and power AP Physics Part 1

2. Power
Power is simply work per time — how many Joules of work you do each second.
Originally people used animals to do work — like oxen. Horses are actually more powerful — they go faster and can do more work per time — but the ox bows used to harness oxen tended to strangle or kill a horse.
This can negatively impact the horse’s performance.

3. Power
The invention of the horse collar allowed farmers to harness horses, which could then generate 50% more power (as well as working longer hours).

4. W P = Dt Power Power is easy: Power = work / time
Power has its own unit, the Watt, named after James Watt, the 17th-18th century inventor who helped improve the steam engine.
One Watt is one Joule/second.

5. Problems
An engine does 1,700J of work in 25 seconds. How much power does it develop?
P = W/Dt
P = 1,700J/25s = 68W

6. Power Watt invented his own unit of power — but it wasn’t the Watt.
How else do we measure power?
Watt invented the horsepower, or hp.
One hp = 746 Watts

7. Variant Power Equations
The basic equation for power is:
Pavg = W/Dt
We usually drop the “avg” (average) and the D and just say:
P = W/t
…but there are other ways to say work:
W = Fr
W = (Fcosq)r
W = Ug = mgh

8. Variant Power Equations
Let’s start with this definition of work:
W = FDr
Drop this into P = W/Dt to give us:
What is Dr/Dt?
P =
FDr Dt
FDr
P = Dt

9. Variant Power Equations
FDr Dt
Dr/Dt is velocity! So power is:
P = Fv
Force times velocity. Or, if the force is at an angle to the motion:
P = Fvcosq

10. Variant Power Equations
P = W/t
P = Fv
P = Fvcosq
Power depends on work and time. The faster you do the work, the more power you develop. The work may be the same, but if you do the same job in half the time you are twice as powerful.

11. Problems
A human fly scales a 350m building. It takes the 52kg daredevil 18 minutes to make the climb. How much power did he develop?
Power is work done over time…
Work done = mgh
P = (52kg)(9.8)(350m)/((18min)(60 sec/min))
= 170W

12. Problems
A 47kg bike rider can develop a max of 0.26hp of power. She rides a Featherlite 250 bike with a mass of 2.3kg. How long does it take her to climb a 235m hill?
Same equation but solve for “t”
P = W/t so t = mgh/P and one hp = 746 Watts
P = (0.26hp)(746W/hp) = 194W
t = (47kg+2.3kg)(9.8)(235m)/194W = 590s

13. Problems
A 15.5kg block is pulled across a flat deck at a constant speed of 3.0m/s, The coefficient of friction is How much power is needed?
Force of pull = force of friction
n = mg so f = mkn or mkmg = (0.330)(15.5kg)(9.8) = 50.1N
Use P = Fv
P = Fv = (50.1N)(3.0m/s) = 150W

14. Problems
An elevator masses 1250kg and can carry a max load of 995kg; there is also a 3850N frictional force. What power is required to lift it at a constant speed of 3.50m/s? In hp, wiseguy???
Total force is total weight plus friction…
P = (mtotalg + f)v
P = ((995kg kg)(9.8) N))(3.50m/s)
= 90,480W = 121 hp

15. Problems
A peculiar design of spaceship uses three rockets each set at a 30° angle. Each generates 10,000,000N of force. (a) If it is 210 km to orbit, how much work is done launching one of these ships to orbit? (b) It takes 15 minutes to get to orbit. How many horsepower does this spaceship develop?
30°
Wone rocket = Frcosq
Wtotal = 3(10,000,000N)(210,000m)cos30°
W = 5.5x1012 J

16. Problems 30° P = W/Dt P = 5.5x1012J/((15min)(60sec/min)) = 6.1X109W
A peculiar design of spaceship uses three rockets each set at a 30° angle. Each generates 10,000,000 of force. (a) If it is 210 km to orbit, how much work is done launching one of these ships to orbit? (b) It takes 15 minutes to get to orbit. How many horsepower does this spaceship develop?
P = W/Dt
P = 5.5x1012J/((15min)(60sec/min)) = 6.1X109W
1 HP = 746W
P = 8.2x106 hp