Drink 633kJ (Monster Energy 340 ml) /20 = m (Push the chair for 31 km!)
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1 Work-Energy-Power Page 1 Work (Ch 16) Work, Energy, is measured in JOULES W = F * S (Joules) = (Newtons) * (Metres) ONLY IF THE DISTANCE IS IN SAME DIRECTION AS FORCE! Note: Torque is in Nm Joules is in Nm?????????? These are NOT the same because... Torque: N is perpendicular to m Work: N is parallel to m Push a Chair along the floor... 20J = 20N * 1m Drink 633kJ (Monster Energy 340 ml) /20 = m (Push the chair for 31 km!) Person weighs 70kg climbs a 400m high tower. Energy? W = F * S W= (70*9.81) * 400 = 274,680 J (About a "Monster") PE = mgh (gravity only!). Full name = Gravitational Potential Energy Work, Energy, is measured in JOULES W = T * Angle (Joules) = (Newton-metres) * (Radians-a ratio = non-units) Flywheel does 200 revolutions with a torque of 35 Nm. Find Work done. W = T * Angle 200 revs = 200 * 2 * pi = rad W = 35 * = J (43.98 kj) POWER P = W / t (Watts) = (Joules) / (s) So if W = FS then P = F*S/t = Fv Also in rotation P = T
2 Work-Energy-Power Page 2 P = T E.g. Keep moving the chair at 1 m/s P = W/t = 20 / 1 = 20 W Electrical motor (12V) P = VI I = P/V = 20/12 = Amps Human power: Cyclist 400W high for W/kg James Watt measured Horse Power. (1 HP = 736 W) Hawkesbury Lookout: Height = 200m, Time 8:43 W = F * S Pretend a ladder W = (68+9)*9.81 * 200 = 151,074 J If ladder guy does it in 8:43 min, what is his power? Seconds = 8* = 523 s P=W/t = 151,074 / 523 = W BTW: How fast is the ladder guy going? s= 200m, t = 523secs: V=s/t = 200/523 = m/s Notice the bicycle was 333W, but ladder is 289W. (Air friction and rolling friction) Work and Acceleration: You may want to use this formula sometimes - or you may not. W = 0.5 * m (v 2 - v o2 ) E.g. A car accelerated from rest to 72 km/h in 16s. Mass = 1.2t Find Power. Linear motion: vo = 0, v1 = 72/3.6 = 20 m/s, t = 16s, a? V = vo+at a = (v-vo)/t = 20 / 16 = 1.25 m/s 2 F= ma = 1200 * 1.25 = 1500 N W = FS Find distance S: (linear motion) S = v 2 / 2a = 20^2 / (2 * 1.25) = 160 m W = FS = 1500 * 160 = J Average Power: P = W/t = / 16 = W (15 kw) Try a faster car: 0-100km/h in 4s. Tesla Roadster 1235kg
3 Work-Energy-Power Page 3 Linear motion: vo = 0, v1 = 100/3.6 = m/s, t = 4s, a? V = v o +at a = (v-v o )/t = / 4 = m/s 2 F= ma = 1235 * = N W = FS Find distance S: (linear motion) S = v 2 / 2a = ^2 / (2 * ) = m W = FS = * = J Average Power: P = W/t = /4 = W (119 kw) This is so boring!! Let's try the super-duper energy method... Work out KE when at 100km/h KE = 0.5*1235* ^2 = J (476.5kJ) This took 4s, so power = W/t = / 4 = kw See? Told you that energy is a marvelous method for the benefit of mankind and gives you goose bumps...
4 Work-Energy-Power Page 4 Springs Tuesday, 1 May :12 PM F = kx k = spring constant (N/m) X = displacement (deformation) F = force (N) Force is increasing as the spring is compressed/stretched. So average force = (F0 + F1) / 2 WORK (or energy stored) of a SPRING W=FS (where force is average) W = 0.5 * kx 2 Example: A spring is stretched 12mm. Spring constant is 200N/mm. Find F: Convert 200N/mm to N/m. k = 200*1000 = N/m, (in m) F = kx = *0.012 = 2400 N (in mm) F = kx = 200 * 12 = 2400 N W = 0.5 * kx 2 = 0.5 * *0.012^2 = 14.4 J (See p244) Watch out! W = FS = 2400*0.012 = 28.8 J (Supposed to be 14.4!!!!)
5 Energy (Ch 17) All types of energy are measured in Joules Potential Energy PE = mgh m = mass (kg) g = gravity accel m/s 2 h = height (m) E.g: Climb up a ladder; Hawkesbury Lookout: Height = 200m, Time 8:43 Pretend to climb up by a ladder W = F * S W = (68+9)*9.81 * 200 = 151,074 J Now use PE formula: PE = mgh W = (68+9)*9.81 * 200 = 151,074 J Exactly the same! So PE = mgh is really just W=FS where F=mg! Wow! Exciting! Kinetic Energy (Linear) KE = 0.5mv 2 m = mass (kg) v = velocity (m/s) Fall off that cliff from top of ladder What speed at bottom? (Well, just before the bottom ) v 0 = 0, s = 200m, a = 9.81m/s 2, v =? v 2 = v as = 2 * 9.81 * 200 = 3924 So square root.. v = 3924^0.5 = m/s (which is *3.6 = km/h) Ouch! What is KE? KE = 0.5mv 2 = 0.5 * (68 + 9) * ^2 = 151, J Wow! It's the same as the PE we got when we climbed up 151,074 J Kinetic Energy (Rotational) KE = 0.5I Work-Energy-Power Page 5
6 Work-Energy-Power Page 6 KE = 0.5I 2 I = Mass moment of Inertia (kgm 2 ) = velocity (rad/s) Check units: (kg * m * m ) * (1/s) * (1/s) = kgm 2 /s 2 This is supposed to be Joules. W = FS = mas = kg * m* (1/s) * (1/s) * m = kgm 2 /s 2 Yes! Same units! So a Joule is kgm 2 /s 2, which is why we call it Joules! Spring Energy SE = 0.5kx 2 k = Spring constant (N/m) x = displacement or deformation (m)
7 Work-Energy-Power Page 7 Spring Energy Tuesday, 30 April :41 PM Q8: (cont) A mass of 491grams stretches this spring by 25mm. How much work did the mass apply to the spring? k = (0.491*9.81) / 25 = N/mm SE = 0.5 k x 2 = 0.5 * * 25^2 = "Nmm" = /1000 = J To show you how dangerous it is NOT to use m k = (0.491*9.81) /0.025 = N/m SE = 0.5 k x 2 = 0.5 * * 0.025^2 = J Kinetic Energy Q15: Calculate the kinetic energy of a 1.4 tonne car at 82 km/h. v = 82/3.6 = m/s KE = 0.5 *1400* ^2 = kj v = 164/3.6 = m/s KE = 0.5 *1400* ^2 = kj Q9: In raising the bucket a force of 192N was applied to the handle (radius 360mm). After 46 revolutions, how much work has been done? Looking only at the handle itself: Using W = T* T = F*r = 192*0.36 = Nm = 46*2*pi = rad W = T* * = 19,978 J ( kj)
8 Work-Energy-Power Page 8 Flywheel Generator Tuesday, 17 March :50 PM Q17: This flywheel has a mass moment of inertia of 0.2 kgm² and rotates at RPM. Calculate the kinetic energy *pi/30 = rad/s KE = 0.5I 2 = 0.5*0.2*5455.9^2 = E6 J = MJ Q18: This flywheel has a mass moment of inertia of 0.21 kgm² and rotates at RPM. What power could it supply for 27s if RPM reduces to 75%? At 100% speed 51200*pi/30 = rad/s KE = 0.5I 2 = 0.5*0.21*5361.7^2 = E6 J At 75% speed 51200*pi/30 = rad/s KE = 0.5I 2 = 0.5*0.21* ^2 = E6 J Total Energy lost = E E6 = E6 J P = W/t = E6/27 = 48911W (48.9 kw)
9 Work-Energy-Power Page 9 Car Hoist Tuesday, 17 March :05 PM Q20: A garage hoist lifts a 1.7 tonne car up through a height of 1.9m. (a) How much work was done to lift the car? W = FS = mgh (same as PE) PE = mgh = 1700*9.81*1.9 = J Q21: (cont) A garage hoist lifts a 1.7 tonne car by 1.9m. (b) If it takes 19 seconds, what was the power applied to lift the car? Time t = 19s P=W/t = /19 = W
10 Work-Energy-Power Page 10 Lathe Tuesday, 17 March :14 PM Q26: During a lathe turning operation, which force (or forces) on the cutting tool are directly opposing the work being done? Work is only done if the force is in same direction as the motion Q27: Shaft diameter=78mm, length=484mm. F1=270N, F2=1630N, F3= 550N. (a) How much work was done by the leadscrew in moving the tool horizontally? Which Force? F1, F2 or F3? Work = F * S = 550 * = J Q28: (cont) Diameter=78mm, length=484mm. F1=270N, F2=1630N, F3 =550N. Feed=0.33mm. (b) How much work was done by the headstock in rotating the job? Which Force? F1, F2 or F3? Work = F * S S = distance of the tool on the job = the length of the whole spiral = how many revs*circumference. Revs = 484/0.33 = revs Circumference = pi*0.078 = m S = * = m Work = F2 * S = 1630 * = J Q29: (cont) Diameter=78mm, length=484mm. F1=270N, F2=1630N, F3 =550N. Feed=0.33mm. Cutting Speed=19m/min. (c) How much time does it take to do the cut?
11 Work-Energy-Power Page 11 does it take to do the cut? Find time. Cutting speed = 19m/minute / 19 = minutes = *60 = 1135 s Q30: (cont) Diameter=78mm, length=484mm. F1=270N, F2=1630N, F3 =550N. Feed=0.33mm. Cutting Speed=19m/min. (d) What power is needed to rotate the shaft during the cut? (Ignore leadscrew) Find power P = W / t = / 1135 = W
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