Physic 231 Lecture 12

Transcription

1 Physic 3 Lecture Main pints last lecture: Cnservative rces and the Cnservatin energy: + P + P Varying rces ptential energy a spring P x Main pints tday s lecture: Wr, energy and nncnservative rces: W Pwer + P P nncnservative W P ; P t Fv

2 Cnceptual prblem Tw marbles, ne twice as heavy as the ther, are drpped t the grund rm the r a building. Just bere hitting the grund, the heavier marble has a) as much inetic energy as the lighter ne. b) twice as much inetic energy as the lighter ne. c) hal as much inetic energy as the lighter ne. d) ur times as much inetic energy as the lighter ne. e) impssible t determine

3 Wr and ptential energy r a spring F spring, x; is The rce is a spring is nt cnstant: x Let s mve the mass attached belw by hand rm x t x with cnstant velcity. This means F hand +F spring, F hand -F spring x the spring cnstant F hand x x x x The P is the area under this curve. It is a triangle: A/ base height P ( x) x x

4 xample The spring abve is stretched rm it equilibrium length x t a maximum length x max. m, then it is released. The spring cnstant is N/m. What is the speed a.5g mass when it returns t the equilibrium length? P x,p a) x - m/s b) x - m/s c) x -3 m/s d) x - m/s v x, + P m x mv v mv + P m x.m / s

5 Cnceptual quiz A spring-laded ty dart gun is used t sht a dart straight up in the air, and the dart reaches a maximum height 4 m.the same dart is sht straight up a secnd time rm the same gun, but this time the spring is cmpressed nly hal as ar bere iring. Hw ar up des the dart g this time, neglecting rictin and assuming an ideal spring? a) 48 m b) 4 m + P,gravity + P,spring c) m + P,gravity + P,spring d) 6 m P P e) impssible t determine mgh mgh mgh,gravity x x x,spring h x x h 4 4m

6 Wr-energy therem with bth cnservative and nn-cnservative rces The wr-energy therem: W Wcns + Wnn cns Fr cnservative rces, W - P: ( P P ) W mech nn cns + W + P nn cns + P P mech, mech,

7 xample A basetball mass.6 g is drpped rm rest rm a height. m. It rebunds t a height.69 m. Hw much mechanical energy was lst during the cllisins with the lr? Mechanical energy + P Initially and at tp bunce : mech lst lst P P P.6g(9.8m / s mg( y y )(.m.69m) ) mech 3.J

8 Pwer Pwer is the rate at which wr is being dne. W P t I we chse the x-axis t lie alng the rce and displacement is characterized by an average velcity: v P W t F x t x F v x The SI units r pwer are J/s W (Watts). Anther unit is hp (hrsepwer). hp 746 W.

9 Bicycle challenge rules Cntestants must warm up by riding r s at P > W. Then each cntestant is judged by the pea r maximum pwer generated anytime in the next s. Can I have tw vlunteers? Shuld the instructr participate? a) yes b) n Carmichael (Armstrng s cach) tld me that a decent pr cyclist wuld have put ut at (an average pwer)least ur hundred watts (during a 4 hur perid), and that the stragglers at the end the peltn (nwn as the gruppett) wuld clc in at perhaps three hundred and ity. Armstrng in tp Tur shape wuld have cme clse t ive hundred. (rm New Yrer article)

10 xample A 5.-g student climbs a 5.-m-lng rpe and stps at the tp. (a) What must her average speed be in rder t match the pwer utput a -W light bulb? P P W mgvy vy.4m / s mg 5g(9.8m / s ) (b) Quiz: Hw much wr des she d? a) 45 J b) 45 J c) 4.5 J d).45 J

11 xample A car accelerates unirmly rm rest t 9 m/s in s alng a level stretch rad. Ignring rictin, determine the average pwer required t accelerate the car i the weight the car is.x 4 N. P t.x ( 9.8m / s ) ( 9m / s) 4 N 4 mv t s 4.3x W

12 xample A sier starts rm rest at the tp a hill that is inclined at with + P P Wnn cns the hrizntal. The hillside is m lng, and the ceicient rictin between ; snw and sis is.75. At the bttm the hill, the snw is level and the ceicient rictin is unchanged. What P ( ) ( )sin( ) is the P mg y y mg m distance d that the sier glides alng the hrizntal prtin the snw bere cming Wnn cns t rest? W, hill + W, lat W (m) µ N (m) µ mg cs( )(m) h W m, hill, lat mg(m)sin( mg(m)sin( (m)sin( d µ mgd sin( (m) µ ) µ mg cs( ) µ cs( ) + µ mg cs( ) cs( )(m) ) )(m) µ mgd )(m) µ d m( µ mgd.94) 74m.