lec05-06-203-11Energywk

lec05-06-203-11Energywk - Kinetic Energy (energy of motion)...

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5/6-1 Kinetic Energy (energy of motion) E or KE 2 2 2 2 x y z 11 K = m v = m(v + v + v ) 22 2 2 m [kg ] J s (Joule) example baseball m=0.15 kg Units pitched at v = 69 mph = 36.5 m/s 2 [kg (m/s) ] mv = (0.15)(36.5) K = 100 J v = 69 mph v = 100 mph K = 210 J !!! Lethal energies
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F || F d d F d W= F d component (projection of) d along F OR Work done by force F acting over displacement d W= F d cos( ) F component (projection of) F along d W= F d !! J s m Kg m ) s m (Kg m (N) 2 2 2 Units 5/6-2
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5/6-3 Collinear F and d Note kinetic friction force always opposes displacement always does - work Constant force not // d example F W= -F d W= +F d F d d box on frictionless plane mg N T d Nd d T T || =T cos( ) note W tot =T || d=T cos( ) d
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h T mg d F = T - mg d = h Work done by gravity W g = mgh Work done by tension W T = Td = -Th Total Work Done on Object W = (T - mg) h W = W g - W T Net Work If object lowered with constant velocity, then mg - T = 0 and W =0 If object accelerates down, then 0 < W < mgd (positive work) (negative work) Ex: object lowered on a string 5/6-4
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0 v - v a= t Work-Energy Theorem Object: m; constant force F; constant accelertation a=F/m 0 v = v + at 0 v + v x =[ ] t 2 W = F x = ma x 00 v - v v + v W = m ( ) {[ ] t} t2 2 2 0 m W = (v - v ) 2 2 2 0 11 W = mv - mv 22 2 1 mv = K = Kinetic Energy 2 0 W = K -K W = K Total work done on object= change in kinetic energy (work done by total force) ) 2 2 m [K]= kg ( Joule = Nm s ) 2 2 ft [K]= slug ( ft lb s or true for non-const. a also !!! 5/6-5
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SI unit: J/s = watt, W 1 horsepower = 1 hp = 746 W A measure of the rate at which work is done. Power= work per unit time [ J/s= Watt] W P = t Average Power dW P = dt Instantaneous Power Power 5/6-6
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m F 10 N d 3m 5 kg W = F || d = 10 (3) Nm = 30 J Assume: no other forces (no friction) & starts from rest (v i = 0) v f 2 = 3.5 m/s W= K What is v f ? W= F d = ½ mv f 2 - ½ mv i 2 30 J = ½ (5 kg) v f 2 If it this took 3 sec what was the average power input by F ?
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lec05-06-203-11Energywk - Kinetic Energy (energy of motion)...

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