Chapter 3 and Chapter 4


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1 Chapter 3 and Chapter 4
2 Chapter 3 Energy
3 3. Introducton:Work Work W s energy transerred to or rom an object by means o a orce actng on the object. Energy transerred to the object s postve work, and energy transerred rom the object s negatve work. F r W The SI unt o energy s joule (J),
4 3.. Denton 3. INETIC ENERGY netc energy s energy assocated wth the state o moton o an object. The aster the object moves, the greater s ts knetc energy. When the object s statonary, ts knetc energy s zero. mv 3.. Worknetc energy theorem Denton W W
5 3..3 Work done by a general varable orce x W F( x) dx x
6 3..4 Work done by a sprng orce Hooke s Law F s kd F x kx Workdone x W F( x) dx x x x kxdx W s kx kx
7 3..5 Work netc Energy Theorem x W ) F( x dx x x x madx dv madx m dx dt From the chan rule o calculus we have dv dt dv dx dx dt v dv dx madx mvdv W v v mvdv W mv mv
8 3..6 Power The tme rate at whch work s done by a orce s sad to be the power due to the orce. As a result: Average power P ave W t Instantaneous power P dw dt
9 Example (3.0) One end o a horzontal sprng k = 80N/m s held xed whle an external orce s appled to the ree end, stretchng t slowly rom x A = 0 to x B = 4.0cm. (a) Fnd the work done by the external orce on the strng. b) Fnd the addtonal work done n stretchng the sprng rom x B = 4.0cm to x C = 7.0cm Soluton W s kx kx W 0.064J ExternalForce J
10 Example (3.0) A 6.00kg block ntally at rest s pulled to the rght along a horzontal rctonless surace by a constant horzontal orce o magntude.0n. Fnd the speed o the block ater t has moved 3.00m. Soluton W mv W 36J v 3.46m / s
11 Example (3.03) A massless sprng that has a orce constant o 000N/m s placed on a table n a vertcal poston. A block o mass.60kg s held.00m above the ree end o the sprng. The block s dropped rom rest so that t alls vertcally onto the sprng. By what maxmum dstance does the sprng compress? Soluton W W net F r kx g ( mg) ˆ.( j d) ˆj kx (000) (.6 9.8)( d) d 500d 5.7d 5.7
12 Snce total knetc energy s zero d 5.7d 5.7 d 0. 9m or d 0. 6m d 0. 9m Example (3.04) A block o mass 6.00kg ntally at rest s pulled to the rght by a constant horzontal orce wth magntude.0n. The coecent o knetc rcton between the block and the surace s Fnd the speed o the block ater t has moved 3.0m. v.78m/ s
13 3.3 CONSERVATION OF ENERGY 3.3. Conservatve and nonconservatve orces A conservatve orce s a orce between members o a system that causes no transormaton o mechancal energy to nternal energy wthn the system. The work done by a conservatve orce s ndependent o the path ollowed by the members o the system and depends only on the ntal and nal conguratons o the system. It ollows that work done by a conservatve orce when a member o the system s moved through a closed path s equal to zero. e.g gravtatonal orce, sprng orce
14 A orce that s not conservatve s called a nonconservatve orce. e.g. knetc rctonal orce and drag orce. e.g. a block sldng across a loor that s not rctonless. Durng the sldng, a knetc energy s transerred to thermal energy or heat (whch has to do wth the random motons o atoms and molecules) Ths energy transer cannot be reversed by the knetc rctonal orce.
15 3.3. Conservaton o mechancal energy E mec U The mechancal energy E mec o a system s the sum o ts potental energy U and the knetc energy o the objects wthn t: Ths prncple o conservaton o mechancal energy s wrtten as: In an solated system where only conservatve orces cause energy changes, the knetc energy and potental energy can change, but ther sum, whch s the mechancal energy o the system, cannot change. U 0 ( U U) U U
16 3.3.3 Conservaton o energy The total energy E o a system (the sum o ts mechancal energy and ts nternal energes, ncludng thermal energy) can change only by amounts o energy that are transerred to or rom the system. Ths expermental act s known as the law o conservaton o energy. E E
17 Example (3.05) A.0 kg box sldes along a loor wth speed v = 4.0 m/s. It then runs nto and compresses a sprng, untl the box momentarly stops. Its path to the ntally relaxed sprng s rctonless, but as t compresses the sprng, a knetc rctonal orce rom the loor, o magntude 5 N, acts on the package. I k =0 000 N/m, by what dstance d s the sprng compressed when the package stops? Soluton U T U T U T mv 0 0 U T 0 kd F r d mv kd F r d d 5d 6 d 5. 5cm
18 Usng the Worknetc energy theorem mv W s kd W r r d W mv kd F r d mv kd F r d d 5d 6 d 5. 5cm
19 Chapter 4 Momentum, Impulse and collsons
20 4. LINEAR MOMENTUM AND ITS CONSERVATION The lnear momentum p o a partcle or an object that can be modeled as a partcle o mass m movng wth a velocty v s dened to be the product o the mass and velocty. p mv I no net external orce acts on a system o partcles, the total lnear momentum o the system cannot change. Ths result s called the law o conservaton o lnear momentum. It can also be wrtten as p p
21 4. IMPULSE AND MOMENTUM The rate o change o the momentum o a partcle s equal to the net orce actng on the partcle and s n the drecton o that orce. dp Fnet dt t t Fdt dp t The rght sde o ths equaton gves us the change n momentum: The let sde, whch s a measure o both the magntude and the duraton o the collson orce, s called the mpulse o the collson. I t t t Fdt
22 4.3 COLLISIONS When two objects collde and stck together ater a collson, the maxmum possble racton o the ntal knetc energy s transormed; ths collson s called perectly nelastc collson. An elastc collson s dened as one n whch the knetc energy o the system s conserved (as well as momentum). The mportant dstncton between these two types o collsons s that the momentum o the system s conserved n all cases, but the knetc energy s conserved only n elastc collsons.
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