Power

1
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

2
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

3
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

4
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

5
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

6
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

7
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!!

8
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

9
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.

10
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

11
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.

12
2a-2

• Ramp angle is about 11.5 degrees (use calculator).

750 m
150 m
13
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.

14
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)

15
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.