Transcript Power & Energy

Power & Energy
• Energy = Power x time
• Assume person can output 50 watts of
useful power for a 10 hour day.
• 1 watt = 1 joule/ 1 second
• 4186 joules = 1 food calorie
• ?joules in 1 day of work?
• E = Pt = (50watts)(10h)(3600s/h) =
1,800,000 joules
1
How much food?
• 1,800,000 joules /(4186 joule/Cal) = 430
Calories.
• Actual consumption? ~ 5x430 = 2150 Cal.
• Food Calorie = Cal = kcal = 1000 cal
• Actual calorie unit is just “cal”
2
How fast?
•
•
•
•
•
•
P = 50 watts
Block m = 100kg mg = 1000 N
Assume f = mg/2 = 500 N
P = E/t = Work/t = Fd/t = F(d/t) = Fv
50 watts = (500 N)(v)
V = 50watts/500N = 0.1m/s
3
blocks
• Density = 2g/cm3 = 2000kg/m3.
• Volume = width x height x depth
= (1.5)(1.0)(2/3) = 1.0 m3.
• Mass = density x volume
= (2000kg/m3)(1.0 m3) = 2000kg
• W = mass x gravity = (2000kg)(10N/kg)
= 20,000 N
4
Force to pull block
• Estimate that it takes half* weight to pull
the block: 10,000N
• Each person pulls ~ 200N for the 5km.
• #people x 200N = 10,000N
• #people = 50
• Power = force x velocity
• 50 watts = 200N x v: v = 0.25 m/s
• * i.e. frictional coefficient = 0.5
5
Time to pull block
•
•
•
•
Distance = velocity x time
5000m = 0.25m/s x time
Time = 20,000 seconds
= 20,000s/3,600s/h = 5.5 hours
• Time to return for another one!:
• Time = 5000m/1m/s = 5000s = 1.5 hour
6
Volume of pyramid
• Volume = 1/3 base x height
• = 1/3 x (230m)2 x 150m = 2,645,000 m3.
• - cavities, estimate 2,000,000 blocks!!
7
Raising a block
• Now we need a force equal to all the
weight
• This doubles the force needed.
• Work = force x distance
• Example: raise 1 block 100meters high.
• Work = weight x 100m
= 20,000N x 100m = 2,000,000 joules
8
Ramp used to raise block.
• Ramp is a simple machine. The principle
is the same as for leverage (torque):
• fD = Fd
• small force f applied for large distance D
equals a large force F over a short
distance d.
• If double # people raise block (100) they
could move it straight up.
9
2a-1
• 100 people moving it up seems too high.
• Lets say 20 people move it up ramp, each
pulling with 200N force.
• fD = Fh
• f = 20 x 200N, D = distance along ramp
• F = 20,000N, h = 150meters height
• (20x200)(D) = (20,000)(150)
• D = 750m
10
Force to go up ramp:
• About equal to (weight of block)/5 + some
frictional force which is probably about
equal to (weight of block)/4.
• Previous slide neglect friction.
11
2a-2
• Ramp angle is about 11.5 degrees (use
calculator).
750 m
150 m
12
reminders
•
•
•
•
•
Quiz III, ch. 7-9, April 11 (Wednesday)
Pyramid Report: Due April 18.
Do I need to type out questions? Yes
All text should be typed.
Formulas can be hand written.
13
review1
• Calculate times: vt = distance
• T1(drag one block to pyramid):
5000meters/(e.g. 0.25m/s) =20000s
=about 5.5h.
• T1’ (walk back): 1.5h
• T2(drag block to average height = 1/3 total
height, i.e. 50m)
14
review2
• Figure total effort in Mh (man-hour) to
move one block all the way to pyr. And up
50m and walk back for another block.
• E.g. 50Mx7.5h = 375 Mh for one block
• 3,000,000 x 375 Mh = 1.1x109 Mh.
• Mh/(20,000h) = 56,000 people.
15