Power Energy Energy Power x time Assume person

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 = (50 watts)(10 h)(3600 s/h) = 1, 800, 000 joules 1

How much food? • 1, 800, 000 joules /(4186 joule/Cal) = 430 Calories. • Actual consumption? ~ 5 x 430 = 2150 Cal. • Food Calorie = Cal = kcal = 1000 cal • Actual calorie unit is just “cal” 2

How fast? • • • P = 50 watts Block m = 100 kg 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 = 50 watts/500 N = 0. 1 m/s 3

blocks • Density = 2 g/cm 3 = 2000 kg/m 3. • Volume = width x height x depth = (1. 5)(1. 0)(2/3) = 1. 0 m 3. • Mass = density x volume = (2000 kg/m 3)(1. 0 m 3) = 2000 kg • W = mass x gravity = (2000 kg)(10 N/kg) = 20, 000 N 4

Force to pull block • Estimate that it takes half* weight to pull the block: 10, 000 N • Each person pulls ~ 200 N for the 5 km. • #people x 200 N = 10, 000 N • #people = 50 • Power = force x velocity • 50 watts = 200 N x v: v = 0. 25 m/s • * i. e. frictional coefficient = 0. 5 5

Time to pull block • • Distance = velocity x time 5000 m = 0. 25 m/s x time Time = 20, 000 seconds = 20, 000 s/3, 600 s/h = 5. 5 hours • Time to return for another one!: • Time = 5000 m/1 m/s = 5000 s = 1. 5 hour 6

Volume of pyramid • Volume = 1/3 base x height • = 1/3 x (230 m)2 x 150 m = 2, 645, 000 m 3. • - cavities, estimate 2, 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 100 meters high. • Work = weight x 100 m = 20, 000 N x 100 m = 2, 000 joules 8

Ramp used to raise block. • Ramp is a simple machine. The principle is the same as for leverage (torque): • f. D = 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

2 a-1 • 100 people moving it up seems too high. • Lets say 20 people move it up ramp, each pulling with 200 N force. • f. D = Fh • f = 20 x 200 N, D = distance along ramp • F = 20, 000 N, h = 150 meters height • (20 x 200)(D) = (20, 000)(150) • D = 750 m 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

2 a-2 • Ramp angle is about 11. 5 degrees (use calculator). 750 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

review 1 • Calculate times: vt = distance • T 1(drag one block to pyramid): 5000 meters/(e. g. 0. 25 m/s) =20000 s =about 5. 5 h. • T 1’ (walk back): 1. 5 h • T 2(drag block to average height = 1/3 total height, i. e. 50 m) 14

review 2 • Figure total effort in Mh (man-hour) to move one block all the way to pyr. And up 50 m and walk back for another block. • E. g. 50 Mx 7. 5 h = 375 Mh for one block • 3, 000 x 375 Mh = 1. 1 x 109 Mh. • Mh/(20, 000 h) = 56, 000 people. 15