Sample Test 3. STUDENT NAME: STUDENT id #:

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1 GENERAL PHYSICS PH -3A (Dr. S. Mirv) Test 3 (/7/07) ke Sample Test 3 STUDENT NAME: STUDENT id #: ALL QUESTIONS ARE WORTH 0 POINTS. WORK OUT FIVE PROBLEMS. NOTE: Clearl write ut slutins and answers (circle the answers) b sectin r each part (a., b., c., etc.) Imprtant Frmulas:. Mtin alng a straight line with a cnstant acceleratin v aver. speed = [dist. taken]/[time trav.]=s/t; v aver.vel. = /t; v ins =d/t; a aver. = v aver. vel. /t; a = dv/t; v = v + at; = /(v +v)t; = v t + / at ; v = v + a (i =0 at t =0). Free all mtin (with psitive directin ) g = 9.80 m/s ; = v aver. t v aver. = (v+v )/; v = v - gt; = v t - / g t ; v = v g (i =0 at t =0) 3. Mtin in a plane v = v cs; v = v sin; = v t+ / a t ; = v t + / a t ; v = v + at; v = v + at; 4. Prjectile mtin (with psitive directin ) v = v = v cs; = v t; ; ma = ( v sin cs)/g = (v sin)/g r in = in ; v = v - gt = v sin - gt; = v t - / gt ; 5. Unirm circular Mtin a=v /r, T=r/v 6. Relative mtin v P A v P B v B A a PA a PB 7. Cmpnent methd vectr additin

2 A = A + A ; A = A + A and A = A + A ; A A A ; = tan - A /A ; The scalar prduct A a b = a b c s a b ( a ˆ ˆ ˆ) ( ˆ ˆ ˆ i a j a zk b i b j b zk ) a b = a b a b a zb z The vectr prduct a b ( a ˆ ˆ ˆ) ( ˆ ˆ ˆ i a j a zk b i b j b zk ) iˆ ˆj kˆ a a z a ˆ ˆ a a z ˆ a a b b a a a a z i j k b b z b b b z b b b b z ( a b b a ) iˆ ( a b b a ) ˆj ( a b b a ) kˆ z z z z. Secnd Newtn s Law ma=f net ;. Kinetic rictin k = k N; 3. Static ti rictin s = s N; 4. Universal Law Gravitatin: F=GMm/r ; G= Nm /kg ; 5. Drag ceicient D C A v 6. Terminal speed v t mg C A 7. Centripetal rce: F c =mv /r 8. Speed the satellite in a circular rbit: v =GM E /r 9. The wrk dne b a cnstant rce acting n an bject: W F d cs F d 0. Kinetic energ: K mv. Ttal mechanical energ: E=K+U. The wrk-energ therem: W=K -K ; W nc =K+U=E -E 3. The principle cnservatin mechanical energ: when W nc =0, E =E 4. Wrk dne b the gravitatinal rce: W m g d cs g

3 . Wrk dne in Liting and Lwering the bject: K K K W W ; i K K ; W W i a g i a g. Spring Frce: F k ( H k's law ) 3. Wrk dne b a spring rce: W k k ; i 0 and ; W k s i i s 4. Wrk dne b a variable rce: W F ( ) d W d W 5. Pwer: P avg ; P ; P F v cs F v t d t 6. Ptential energ: U W ; U F ( ) d 7. Gravitatinal Ptential Energ: U m g ( ) m g ; i 0 a n d U 0 ; U ( ) m g i i i i i 8. Elastic ptential Energ: U ( ) k 9. Ptential energ curves: du ( ) F ( ) ; K ( ) E m e c U ( ) d 0. Wrk dne n a sstem b an eternal rce: F ric ti n is n t in v lv e d W h e n k in e tic ric ti n rc e a c ts w ith in th e s ste m E d th k W E K U m e c W E E m e c th. Cnservatin energ: W E E E E m e c th r islated sstem (W =0) E E E 0 in t m e c th in t E. Pwer: P avg ; t P de d t ; 3. Center mass: r m r n i i M i 4. Newtns Secnd Law r a sstem particles: F net M a

4 . Linear Mmentum and Newtn s Secnd law r a sstem particles: P M v and F net dp dt t. Cllisin and impulse: J F ( t ) d t; J F t; t i avg when a stream bdies with mass m and n n m speed v, cllides with a bd whse psitin is ied F avg p m v v t t t Impulse-Linear Mmentum Therem: p p i J 3. Law Cnservatin Linear mmentum: P P r clsed, islated sstem 4. Inelastic cllisin in ne dimensin: p p p p i i i 5. Mtin the Center Mass: The center mass a clsed, islated sstem tw clliding bdies is nt aected b a cllisin. 6. Elastic Cllisin in One Dimensin: m m v v ; v m v i i m m m m 7. Cllisin in Tw Dimensins: p p p p ; p p p p i i i i 8. Variable-mass sstem: Rv rel v v v M a (irst rcket equatin) i r e l M i ln (secnd rcket equatin) M S 9. Angular Psitin: (radian m easure) r 0. Angular Displacement: (p sitiv e r c u n terclc k w ise r tatin ) d. Angular velcit and speed: avg ; (p sitive r c u n tercl ck w ise rtati n ) t d t. Angular acceleratin: avg ; t d d t

5 t ( ) t. angular acceleratin: t t ( ) t t. Linear and angular variables related: v r s r ; v r ; a t r ; a r r ; T r v 3. Rtatinal Kinetic Energ and Rtatinal Inertia: K I ; I m iri r bd as a sstem discrete particles; I r d m r a bd w ith c n tin u u sl distributed m ass. 4. The parallel aes therem: I I M h 5. Trque: rf r F rf sin t 6. Newtn s secnd law in angular rm: net I 7. Wrk and Rtatinal Kinetic Energ: W d ; W ( ) r cnst; i i dw P K K K I I W dt ; i i w rk e n e rg th e re m r r ta tin g b d ie s v K I m v 8. Rlling bdies: a R a R g sin r rlling sm thl dw n the ram p I / M R 9. Trque as a vectr: r F ; rf sin rf r F

6 . Angular Mmentum a particle:. Newtn s Secnd law in Angular Frm: net l r p m( r v); l rmvsin rp rmv r p r mv 3. Angular mmentum a sstem particles: 4. Angular Mmentum a Rigid idbd: L I dl dt L net et n l i i dl dt 5. Cnservatin Angular Mmentum: L L (islated sstem) 6. Static equilibrium: F net 0; 0 7. Elastic Mduli: stress=mdulus strain net i i all the rces lie in plane F 0; F 0; 0 net, net, net, z F L 8. Tensin and Cmpressin: E, E is the Yung's mdulus A L F L 9. Shearing: G, G is the shear mdulus A L 0. Hdraulic Stress: p B V, B is the bulk mdulus V

7 . At the same instant that a 0.50-kg ball is drpped rm 5m abve Earth, a secnd ball, with a mass 0.5 kg, is thrwn straight upward rm Earth's surace with an initial speed 5m/s. The mve alng nearb lines and pass each ther withut clliding. + What is the height abve Earth's surace the center mass the tw-ball sstem at the end.0 s? m v =0 =5m v =5 m/s m 5.4m 0.4m t=0 t=.0s ( a) Find inal crdinate the ball ater.0 s. gt t 5 5.4m (b) Find inal crdinate the ball ater.0 s gt 9.8 vt 5 0.4m (c) Find crdinate the center mass tw balls m m (0.5)(5.4) (0.5)(0.4) 7.m m m ( )

8 . Tw skaters with masses 00 kg and 60 kg, respectivel, stand 0.0 m apart; each hlds ne end a piece rpe. I the pull themselves alng the rpe until the meet, hw ar des each skater travel? (Neglect rictin) 00kg 0m 60kg 0 + ( a) Since tw scaters represent an islated sstem and initiall theu are at rest their center mass will be at rest and the will meet at the center mass m m m m (00)(0) (60)(0) m 3.8m (b) The 00 kg skater mves 3.75 m (c) The 60 kg skater mves =6.5m=6.m

9 3. A kg blck wd rests n a lng tabletp. A 5 g bullet mving hrizntall with a speed 50 m/s is sht int the blck and sticks in it. The blck then slides 70 cm alng the table and stps. (a) ind the speed the blck just ater impact. (b) ind the rictin rce between blck and table. v v 0 =0 m m.7 m (a) Cnsider inelastic bullet-blck cllisin. At the instant cllisn bullet-blck sstem is islated, hence, we can use law cnservatin linear mmentum t describe the cllisin mv mv 0 0 mv 0mv 0 (0.005)(50) ()(0) ( m m ) v ; v m/ s ( m m ) (0.005 ) (b) Calculate wrk dne b the net rce n a blck-bullet sstem during its mtin alng the table There are 3 rces acting n ur sstem: Weight, Nrmal reactin, and kineti rictin. Onl kinetic rictin rce will perrm nn zer wrk. W (c) Mtin a blck-bullet sstem ater the cllisin can be described b a wrk-energ therem net S ( m m ) v ( m m ) v (0005 (0.005 )(0374) )(0.374) net i k 0 k 50 W K K S N S (.70) k

10 4. The impact the head a gl club n a gl ball can be apprimatel regarded as an elastic cllisin. The mass the head the gl club is 0.5 kg. The speed the club bere the cllisin is 46 m/s. The ball acquires a speed 70 m/s ater the cllisin. The gl club and a ball are in cntact r abut 0.5 ms. a) What must be the mass the ball? b) What is the average rce eerted b the club n the ball? (a) Fr elastic gl club-ball cllisin v b mc m m mv (0.5)(46) c ci mb v m b c kg 70 c b v ci P P P (0.047)(70) 0 ( ) t t b bi bfavg N N

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12 6. Je is painting the lr his basement using a paint rller. The rller has a mass.4 kg and a radius 3.8 cm. In rlling the rller acrss the lr Je applies a rce F=6N directed at an angle 35% as shwn. Ignring the mass the rller handle, what is the magnitude the angular acceleratin the rller? F 35 N (a) nd Newtn law ais: s Fsin ma ( b ) nd Newtn Law r rtatin ti abut : R I (c) recall the relatinship between a and : a R; I ( d) substitute eq.(b) and (c) in (a): Fsin m R ; R F sin F sin F sin (6)sin 35 I mr mr mr 3mR 3(4)(0 3(.4)(0.038) 038) R rad 67 s s s mg F

13 7. A hp (I h =MR ), a unirm disk (I d =/MR ), and a unirm sphere (I s =/5MR ), all with the same mass and uter radius, start with the same speed and rll withut sliding up identical inclines. Rank the bjects accrding t hw high the g, least t greatest. ( a)during rlling up the incline mtin the mechanical energ the hp-earth, disk-earth, and sphere-earth sstems is cnserved since )rictinal rce des nt transer an energ t thermal energ because the bjects d nt slide; ) nrmal rce is perpendicular t the pass; 3) gravitatinal rce is a cnservative ne. I Mv 0 0 Mgh ( b) secnd term is the same r all ur bjects, is als the same, the larger I the larger maimum height h reached b the bject. rm least t greatest t in terms height ht attained: sphere, disk, hp.

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15 9. A unirm seesaw length 6 m has tw ungsters weights w =700N and w =400 N sitting n the ends. Find the prper lcatin the pivt r the seesaw t be just in balance, i (a) the weight the seesaw can be ignred (b) the seesaw weighs Mg=300N 6 m w Mg ( a) Use nd cnditin equilibrium: W W(6 ) 0; 6W 6(400).8m W W w ( b )Use nd cnditin equilibrium: WMg(3 ) W(6 ) 0; 6W 3Mg 6(400) 3(300) W W Mg m