Exam1.pdf - Physics 207 058 Exam 1 1 At a certain instant...

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Unformatted text preview: Physics 207 — 058 Exam 1 1. (*) At a certain instant of time, the acceleration and velocity vectors of an object are shown to the right. Which statement mp_st correctly describes the motion of this object? Acceleration March 11th, 2005 it is slowing down and turning upwards (b) it is speeding up and turning downwards (c) it is maintaining its speed but turning upwards (d) it is slowing down but not changing direction (e) it is undergoing uniform circular motion 2. (*) This question and the next question are about the following situation Velocity A 3-kg block sits on a 10-kg'block resting on a frictionless table, as shown. A string along the horizontal direction with a force F pulls the lower block. The two blocks move ahead together with an . 2 acceleratlon of] m/s . ,: W14 3 3(1) 1: 3 A! E19,? a= 1 m/s2 What is the pulling force? (a) F=10N E, (b) F=7.0N c F=16N @F=13N —~3+F: /0(() F‘ e) F=39N 3. (*) What horizontal force does the bottom block exert on the upper block".7 (a) FM = 0.0 N b Fb,u = 7.0 N @ Fb,u = 3.0 N (d) FM = 1.0 N (e) FM = 2.0 N . ‘4 Physics 207 — 05$ Exam 1 March 11th, 2005 4. (**) At the right is a graph of the acceleration of a point particle as a function of time: Accel Which choice below is a possible graph of the [In/52] position of the particle as a function of time? , Tlme [sec] (3) Position [m] \ mm" A [m] Time [sec] (c) Epjition Time [sec] 5. (**) A mass m is attached to a spring with spring constant k, the other end of which is attached to the ceiling. It is pulled and allowed to oscillate up and down. Using dimensional analysis, determine which one of the following is a valid expression for the time, T, it takes to complete each oscillation. (a) T = 21tkm (b) T = 2m/m-k @ = 21: m/k k (d) T = 2m/k3/m (e) T = 21t+m/k2 Physics 207 — 05S Exam 1 March 1 1th, 2005 6. (*) This and the next question are about the following situation. A car undergoing uniform acceleration, a = 3 m/sz, is traveling at a velocity of 36 m/s as it enters a . tunnel. When the car exits the tunnel, its velocity is 60 m/s. How long is the tunnel? (a) 267 m (b) 307 m (c) 346 m g}. 84 m e) 442 In 7. (*) For how long is the car in the tunnel? ins” (b)7.0s 60 = 3Q + 3‘6 __ (c) 6.0 s 3 8. (**) An empty car is driven off of a cliff as part of a stunt for a new movie. The car starts at rest and then undergoes constant acceleration of a = 4.5 m/s2 for a distance of r = 100 m. The car then goes off the cliff, leaving the cliff traveling parallel to the ground. The cliff is a height h = 78.4 m above the ground below. ,4. 1 1 ? 24,. 111‘s U+ : ¢ 1” 2. (7‘5) ((00) a) W i=lfmm «wmmmn & :. ?é 2/g What is the distance D away from the cliff that the car lands? ,—_ (a 108 m f say 0 m ,_ A @0132“) b ~ 30%; 4mm (d) 144 m (e) 156 In Physics 207 — 058 Exam 1 March 11th, 2005 9. (***) Buckingham fountain in Chicago E 3.; 3 has several water jets with the '” “ geometry shown in the figure. The initial speed of the water coming out ofthejet is v0 = 8 m/s. How from the edge of the upper pool does the water fall? This distance is labeled x in the figure. (a) The water does not make it all the way to the upper pool. £53m AX: UOCOSED‘E .m 2. ()3.1m y:p’+ Uofiu8£~ liq-715 2. (e) 4.6m L5. 2 fsc‘k‘fi’é ‘ L/Qf 9.962 — 5:666 H520 Ax: 5.4a (‘5~“‘(2~)=‘f.2,m’ t= {W : iééifi" ii? )4: LLZ‘Z’: 2-2.»... 10. (*) A boat captain guides his boat across the river at an angle 6 as shown. The river flows towards the east. If the speed of the boat with respect to the river, WM, , is 12 mph, the angle 6 = 60° and she ends , of the river? 17. up on the opposite bank directly across from her starting point, what is the speed, ., = 6.0 mph (b) 17, = 10.4 mph (c) 17, = 12 mph (d) 17, =7.2 mph (e) 17, = 8.4 mph Physics 207 — 05$ Exam 1 March 11th, 2005 1 1. (* *) This and the next question are about the following situation: A tennis ball of mass m is attached to a rope and swung in a vertical circle. The rope has a length, L_= 2 m. The weight of the ball is W= 0.5 N. W. M1 ’00 55; When the ball is at its highest point, the tension in the rope is x'” ' :3“ W—0. 5 N p" , 1 N. What is the tangential velocity (speed) of the ball at its ’ ‘ \ 07 K highest point? I/ ‘\\ .; 0‘05’1 (a) V; = 2.8 In/S K :I L: H] ‘II g (b) v, = 4.7 m/s l '-. ," (c) v, = 5.3 m/s Y _ m T \‘\ I, (d v, — 6.8 m/s 3 a (Q ,= 7.7 m/s w. v “ ------ ” T + m = MOL = "‘" j 2. L ground U '—‘~ ¥ G P T—%_M3:l MV51+0§\(~§‘ L.— m 7, .____ 2- I. g — .3— 58 8 12. (*) When the rope is exactly horizontal to the ground the speed of the ball is v. Which of the following expressions for the tension, T, is correct? a T: W @ T=mv2/L (c) T: va/L a W 13. (***) An inclined plane with angle 0 = 30° has a smooth frictionless surface. A mass, m = 5-kg, sits on the plane and is attached by a massless rope strung over a pulley to a hanging mass, M = 7-kg. What is the displacement of mass m two seconds after the system of two masses is released from rest? x v V v (a) 3.7m "I”l L); 7?. (b) 3.0 m 7.4 m (d) 5.6 m M (e) 8.1 m 3 Physics 207-058 Exam 1 Formula Sheet Kinematics v = we + at 2 r=r0+ v0t+ at /2 v2 =v§ +2a(x-xO x-xo= (v0+v)t 2 x-x0 = vt - (”2/2 g = 9.81 m/sl 2D Motion hmax = v? sin2 6/2g Range = vi2 sin 26/g Uniform Circular Motion a=v2/r=0)2r v=03r m=21t/T=27tf Galilean Transformations *l r = r — v0! s, _ . , __ v — 0 Dynamics F’VET = ma FA.B = —F30,1 F = mg (gravity near earth‘s surface) F” =—Gm1m2 r2; G:6.67x10‘“ Nomz/kgz F =—k(Ax) spring sin 6 = l I cos 6 = “v T | v tan 6 — 1 Q 1: x2 +y2 =r2 sin 26 = 25in 6cos¢9 sin 30 = 0.50; cos30° = 0.866 sin 60" = 0.866; cos 60" = 0.50 ifax2+bx+c=0then = —bi\/b2 —4ac 2a A 7 ‘\ x ...
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