Rectaton: Energy, Phys 207. Energy. Energes. An acorn fallng from an oak tree onto the sdewalk. The acorn ntal has gravtatonal potental energy. As t falls, t converts ths energy to knetc. When t hts the ground, the knetc energy s converted nto heat, and vbratonal energy. 2. A baseball durng ts trajectory from home plate to over the rght feld fence. The baseball has knetc energy mmedately after t s ht by the bat. A porton of the knetc energy s transformed nto potental as t rses. Then as t falls back towards the ground, the potental energy s converted back to knetc. 3. A car starts from rest then accelerates to a velocty There s gas n the car's tank. Ths s energy stored n the hydrocarbons n the gas. Combuston of gas releases energy, whch s transformed nto both knetc energy of the car, usng the mechansms n the motor, as well as heat and sound. 4. You eat a plate of spaghett then run up a hll the next day There s chemcal energy stored n the chemcal bonds of the pasta. Your body converts ths to heat, and also knetc energy of your movng lmbs. Ths knetc energy s then turned nto gravtatonal potental as you clmb the hll. 5. A rocket s launched nto orbt There s chemcal energy that s stored n the rocket fuel. Ths s converted nto knetc energy of the movng rocket. As the rocket goes nto orbt, the knetc energy s transformed nto gravtatonal potental. As t orbts, t has both knetc and gravtatonal potental energy..2 Three stones For each case, the ntal mechancal energy wll equal the fnal mechancal energy: The ntal mechancal energy s a combnaton of potental and knetc: The fnal mechancal energy s all knetc, snce the stones wll be at y = 0: = f = KE + U = m v 2 + mgh 2 Equatng these two: Thus, for each case, we can solve for v f :. Case : the stone s launched straght up: 2. Case 2: the stone s launched straght horzontally: 3. Case 3: the stone s launched straght down: f = KE + U = m v 2 + 0 2 f m v 2 + mgh = m v + 0 2 2 2 f = v f = v f2 = v f3 2gh + v 2 2gh + v 2 2gh + v 2 All three cases end wth the same speed. Page
speed One of our knematc equatons was: v 2 = v + 2aΔx f 2 Ths s the same equaton..3 Partcle n a bowl Intal Poston: the partcle s at rest, at some heght above the ground. Fnal Poston: at the bottom of the bowl, the partcles s movng. So, t has a knetc energy value, but we can say ts potental energy s zero at that locaton. h = R( cosθ) The ntal mechancal energy wll be equal to the fnal: = f mgh = mgr( cosθ) = mv 2 2 Thus, we can solve for v: v = 2gR( cosθ) 4 3 2 functon s non-lnear θ v 0 0 m/s 5 0.87 m/s 30.62 m/s 45 2.40 m/s 60 3.3 m/s 75 3.8 m/s 90 4.43 m/s 20 40 60 80 degrees Just solve the conservaton of energy equaton for θ nstead of v: θ = cos v 2 ( ) 2gr Page 2
.4 Energy Conservaton Page 3
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.5 Energy Graphs Page 8
2. Work 2. Some sketches. A marble fallng straght down to the ground n free fall, startng from rest a few meters off Page 9
the ground. 2. A pece of steel s on the ground at a constructon ste. A crane lfts the pece of steel at a unform velocty to a hgh floor of the buldng. 3. The crane s used to to brng a worker from the roof to the ground. 4. A skateboarder rdng down a (frctonless) hll. Page 0
5. A skateboarder who has fallen off the skateboard and s now sldng down the very hgh frcton hll. 6. A car at t travels around a curved road. 2.2 More Work W = ΔKE = m v 2 = 0 5 2 = 25 J 2 f 2 W = F d = F d cosθ = 40 2000 cos 20 = 7575 J The work done wll be 0. (force s to dsplacement) Work s gven by the force tmes the dstance. h s the heght of the ESB. W = F G h = 9.8 38 = 3734 J W = ΔKE = mv 2 m v 2 = Fd cosθ = mgd cosθ 2 f 2 v f = v 2 2mgd cos( 82 ) + = 6.6 m/s m Page