GENERAL PHYSICS PH 221-1D (Dr. S. Mirov) Test 4 (04/29/13) ALL QUESTIONS ARE WORTH 20 POINTS. WORK OUT FIVE PROBLEMS.

Transcription

1 GENERAL PHYSICS PH -D (Dr. S. Mirov) Test 4 (04/9/3) STUDENT NAME: key STUDENT id #: ALL QUESTIONS ARE WORTH 0 POINTS. WORK OUT FIVE PROBLEMS. NOTE: Clearly write out solutions and answers (circle the answers) by section or each part (a., b., c., etc.) Iportant Forulas:. Motion along a straight line with a constant acceleration v aver. speed [dist. taken]/[tie trav.]s/t; v aver.vel. / t; v ins d/ t; a aver. v aver. vel. / t; a dv/ t; v v o + at; /(v o +v)t; v o t + / at ; v v o + a (i o 0 at t o 0). Free all otion (with positive direction ) g 9.80 /s ; y v aver. t v aver. (v+v o )/; v v o - gt; y v o t - / g t ; v v o gy (i y o 0 at t o 0) 3. Motion in a plane v v o cosθ; v y v o sinθ; v o t+ / a t ; y v oy t + / a y t ; v v o + at; v y v oy + at; 4. Projectile otion (with positive direction ) v v o v o cosθ; v o t; a ( v o sinθ cosθ)/g (v o sinθ)/g or y in y in ; v y v oy - gt v o sinθ - gt; y v oy t - / gt ; 5. Unior circular Motion av /r, Tπr/v 6. Relative otion vpa vpb + vba apa apb 7. Coponent ethod o vector addition

2 A A + A ; A A + A and A y A y + A y ; A A + A y ; θ tan - A y /A ; The scalar product A a b abcosφ a b ( aiˆ ˆ ˆ) ( ˆ ˆ ˆ + ay j+ ak z bi + by j+ bk z ) a b ab + ab y y + ab z z The vector product a b ( aiˆ+ a ˆj + akˆ) ( biˆ+ b ˆj + bkˆ) y z y z iˆ ˆj kˆ ay az a ˆ ˆ a a z ˆ ay a b b a a ay az i j + k by bz b b bz by b b b y z ( a b ba ) iˆ+ ( ab ba ) ˆj + ( ab ba ) kˆ y z y z z z y y. Second Newton s Law af net ;. Kinetic riction k µ k N; 3. Static riction s µ s N; 4. Universal Law o Gravitation: FGM/r ; G N /kg ; 5. Drag coeicient D Cρ Av 6. Terinal speed v t g Cρ A 7. Centripetal orce: F c v /r 8. Speed o the satellite in a circular orbit: v GM E /r 9. The work done by a constant orce acting on an object: W Fd cosφ F d 0. Kinetic energy: K v. Total echanical energy: EK+U. The work-energy theore: WK -K o ; W nc K+ UE -E o 3. The principle o conservation o echanical energy: when W nc 0, E E o 4. Work done by the gravitational orce: W gd cosφ g

3 . Work done in Liting and Lowering the object: K K K W + W ; i K K ; W W i a g i a g. Spring Force: F k (Hook's law) 3. Work done by a spring orce: W k k ; i 0 and ; W k s i o i s 4. Work done by a variable orce: W F( ) d W dw 5. Power: Pavg ; P ; P Fv cosφ F v t 6. Potential energy: U W ; U F( ) d 7. Gravitational Potential Energy: U g( y y ) g y; i y 0 and U 0; U( y) gy i i i i i 8. Elastic potential Energy: U( ) k 9. Potential energy curves: du( ) F( ) ; K( ) Eec U( ) d 0. Work done on a syste by an eternal orce: Friction is not involved W E K + U ec When kinetic riction orce acts within the syste W E + E E th d k ec th. Conservation o energy: W E E + E + E ec th or isolated syste (W0) E + E + E 0 int ec th int E. Power: Pavg ; P t de ; 3. Center o ass: r co n r i i M i 4. Newtons Second Law or a syste o particles: Fnet Maco 3

4 . Linear Moentu and Newton s Second law or a syste o particles: P Mv and F co net dp t. Collision and ipulse: J F( t) ; J F t; ti avg when a strea o bodies with ass and n n speed v, collides with a body whose position is ied Favg p v v t t t Ipulse-Linear Moentu Theore: p pi J 3. Law o Conservation o Linear oentu: P P or closed, isolated syste 4. Inelastic collision in one diension: p + p p + p i i i 5. Motion o the Center o Mass: The center o ass o a closed, isolated syste o two colliding bodies is not aected by a collision. 6. Elastic Collision in One Diension: v v ; v v i i Collision in Two Diensions: p + p p + p ; p + p p + p i i iy iy y y 8. Variable-ass syste: Rv rel Ma (irst rocket equation) v v v i rel M i ln (second rocket equation) M S 9. Angular Position: θ (radian easure) r 0. Angular Displaceent: θ θ θ (positive or counterclockwise rotation) θ dθ. Angular velocity and speed: ωavg ; ω (positive or counterclockwise rotation) t ω. Angular acceleration: αavg ; α t dω 4

5 ω ω + αt θ θo ( ωo + ω ) t. angular acceleration: θ θo ωot+ αt ω ω + αθ ( θ) r d o o θ θo ωt ωt. Linear and angular variables related: v πr π s θr; v ωr; at αr; ar ω r; T r v ω 3. Rotational Kinetic Energy and Rotational Inertia: K Iω ; I r i i or body as a syste o discrete particles; I or a body with continuously distributed ass. o 4. The parallel aes theore: I I + Mh co 5. Torque: τ rf r F rf sin t 6. Newton s second law in angular or: τnet I 7. Work and Rotational Kinetic Energy: φ α W θ τ d θ ; W τθ ( θ i) or τ const; θ i dw P K K K Iω Iω W ; i i work energy theore or rotating bodies 8. Rolling bodies: v co K Icoω + v a αr a co co ωr co g sinθ + I / MR co or rolling soothly down the rap 9. Torque as a vector: τ r F; τ rf sinφ rf r F 5

6 l r p r ( v);. Angular Moentu o a particle: l rv sin rp rv r p r v. Newton s Second law in Angular For: τ net 3. Angular oentu o a syste o particles: 4. Angular Moentu o a Rigid Body: L Iω φ dl L τ net et n l i i dl 5. Conservation o Angular Moentu: L L (isolated syste) 6. Static equilibriu: F net 0; τ 0 7. Elastic Moduli: stressodulus strain net i i all the orces lie in y plane F 0; F 0; τ 0 net, net, y net, z F L 8. Tension and Copression: E, E is the Young's odulus A L F L 9. Shearing: G, G is the shear odulus A L V 0. Hydraulic Stress: p B, B is the bulk odulus V. Siple haronic otion: t+ v t+ a t+ cos( ω φ); ω sin( ω φ); ω cos( ω φ) k. The Linear Oscillator: ω, T π k 3. Pendulus: T T T π I, torsion pendulu k π L, siple pendulu g I π, physical pendulu gh 6

7 . Daped Haronic Motion: bt k b t ( ) e cos( ω' t+ φ), ω', Et ( ) ke 4 bt. Sinusoidal waves: y(, t) y sin( k π ω ω λ ωt), k,, v λ λ π T k T 3. Wave speed on stretched string: v τ µ 4. Average power transitted by a sinusoidal wave on a stretched string: Pavg µω v y 5. Intererence o waves: y '(, t) [ y cos φ]sin( k ωt + φ) 6. Standing waves: y '(, t) [ y sin k]cosωt v v 7. Resonance: n, or n,,3,... λ L B 8. Sound waves: v, ρ L φ π ( π) or 0,,, 3..., constructive intererence λ 9. Intererence: L φ π (+ ) π or 0,,, 3..., destructive intererence λ 0. Sound Intensity: P Ps I, I ρω v s, I A 4π r. Sound level in decibels: I β (0 db) log, Io 0 W / I o. Standing wave patterns in pipes: v nv, n,, 3,..., or pipe opened ro both ends λ L v nv, n,3,5,..., or pipe closed at one end and opened at the other λ 4L 3. Beats: beat 7

8 vr. The Doppler eect: ' ( ± ) v sound;(v s 33/s); ' v E v s vs ± vr ' general Doppler Eect v v s E, v R the speed o the receiver; v s the speed o the s + or receiver approaching stationary eitter, - or receiver oving away ro the stationary eitter;, v E the speed o the eitter, v s the speed o the sound, - or eitter approaching stationary receiver, + or eitter oving away ro the stationary receiver; 8

9 9

10 . A transverse traveling sinusoidal wave on a string has a requency o 00Hz, a wavelength o 0.040, and an aplitude o.0. What is a) the aiu velocity in /s o any point on the string? b) the speed o the wave? The absolute value o the aiu velocity o any particle on a string is v ωy π y π(00 Hz) (0.00 ).3 / s pa v λ (0.04 ) (00 Hz) 4 / s wave 0

11 3. I the length o a piano wire (o given density) is increased by 5%, what approiate change in tension is necessary to keep its undaental requency unchanged? TL T.05L v L L (.05 L) T T.05 (.05) T (.05) T T T T(.05 ) 5% increase T T

12 4.

13 5. 3

14 6. Two gol carts have horns that eit sound with a requency 390 Hz. The gol carts are traveling toward one another, each traveling with a speed o 9.0 /s with respect to the ground. What requency do the drivers o the carts hear? The speed o sound at the gol course is 343 /s. vsa + vd Hz v v beat sa S Hz 4