exam1_1997s_sol

exam1_1997s_sol - Name 0 Section P221/S97/Problem 1A [10...

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Unformatted text preview: Name 0 Section P221/S97/Problem 1A [10 points] An object of mass 4.0 kg is located at the origin at time t = 0.00 s, when it has an initial velocity of 3.0 m/s in a direction, in the second quadrant, that makes a 45° angle with the negative 2: axis. It experiences a net force of magnitude 12 N directed along i. Determine the acceleration, velocity, and position of the mass as functions of time, using unit vector notation. The net force acting on the object is FM 2 (12 N)? The acceleration of the object is a = Fuet/m : (12 NT)/(4.o kg) = (3.0 m2)? Since the acceleration is constant, the formulas for constant-acceleration motion can be used. The initial velocity of the object is {50 = (110 cos 6) i + (110 sin (9)? = (3.0 m/s)(cos 135°)? + (3.0 m/s)(sin 135°)? = — (2.1 m/s)i + (2.1 m/s)? The velocity of the object is 17(5) = in + at = — (2.1 m/s + (3.0 m/s‘z) t )T + (2.1 m/sfi The position of the object is 7 ms) = 1707: + $6152 2 — ((2.1 m/s) t + (1.5 n1/32)1f2 )T +(2.1m/s)tj Name Section P221/S97/Problem 1B A 75-kg person standing in a 25-kg lift pulls straight down on a massless rope which goes around two massless, frictionless pulleys and is attached to the top of the lift at the other end, as shown on the diagram. The / person and the lift accelerate upward at a rate of 2.0 m/s2. (a) [3 points] Draw free-body force diagrams for the person and the lift. Label all of the forces using conventional notation. —u i1 a a i t i Mg N2 mfi M = 75 kg is the person's mass and m = 25 kg is the lifl's mass. The tensions T1 and T2 are the same, which we can call T, because they are the same rope. The normal forces N1 and ’ N 2 are a 3rd-law pair, so they have the same magnitude, which we can call N. (b) [5 points] Estimate (to one significant figure) the magnitude of the force exerted by the person on the rope. Remember to justify your estimation, don't just pick an estimate out of the air. This force is just equal to the tension in the rope, T. To determine it, let‘s make use of Newton's second law. The accelerations E1 and 62 of the person and lift, respectively, must be equal since the person and the lift are moving upwards together; let's call the magnitude of this acceleration a. Newton's second law applied to each object gives: person: T+N—-Mg=Ma lift: T—N—mg=ma The unknowns are T and N. By adding these two equations, left side to left side and right side to right side, we can eliminate N by getting 2T— (M+m)g = (M+m)a so = %(M+m)(g+a) = $05 kg+25 kg)(10 m/s,2 +2m/s2) = (so kg)(12 m/s2) = 6 x 102 N or 0.6 kN. (c) [2 points] Suppose the person in the lift is standing on a scale on the lift. Estimate (to one significant figure) the reading on the scale. The scale reading would equal N, the magnitude of the normal force. We can use the two equations in part (b) and subtract the second from the first to eliminate T: 2N—(M—m)g= (M—m)a so N = %(M —— m)(a + g) = %(75 kg — 25 kg)(10 m/s2 + 2 III/S2) = (25 kg)(12 rn/32) = 3 x 102 N or 0.3 kN. Name ___________________ Section P221/S97/Problem 1C .4) T A ball of mass m is thrown from ground A); k level at an angle of 45° to the horizontal. A wall of height h is a distance D from where the ball is thrown, and D > h. Neglect air a resistance. (a) [8 points] Find an algebraic expression for the minimum initial speed of the ball, v0, necessary for the ball to go over the wall. (By "algebraic expression" we mean an expression in terms of such quantities as m, D, h, and 9.) mo mfmsyms FotL Mt) AND we) M We gem/mas 04215114 -. clan-HM ‘fo‘m’l‘ 9W Lama-x n+1 15H! bdA’3 Thaw/J mxevicoée _=> KCH= {mafiafi v... = V; 57MB was) = (US $N©>£ ‘ 12311: AJ— i:=‘b_g' m 5M1 "ewe-(es "M: wML (wiq-gfié (:19) 50 .__3 f; .__ ._3>__ D: @3659) be m '5 mease M’ i: vb; , ’o’c'c mu straws m LAJA’U mt“- \/ > k (we sine) £4 — 32ft: > L‘ gm Qfifim’t‘c i») ou(7~ Exfihsswzd m £4— @sme— D >— é3<$e>z>k VB cage b?— 2 swig—5L >.;——— mb'bkbe"§v%_;_s?g>in =5 zIvazaasze’ O . ,_ ? ,J 5 memormo/‘S émcz 6:45”) £AQ~{SO=\ mm (.05 4° 1/ a :- DL iv 31>; b"L\ 7 fl >i—3—v =5 m D D—k 7. zvé‘o-I) 7% (Continued on the back of this sheet...) Problem 1C, part (b) [2 points] Can the ball clear the wall if D < h? Briefly explain why or why not. <L€ )4 (at Trktn "Ms, gun-Mr} Mlec‘mzAI (bdrm m 2M1 éfikl \lN \A €TP-P5befi‘ LIE/“Q bOéS/LHT (LEA/L 176?. ‘7' b U 5197/: T‘rfi imam/xmmal We fwé I may 2 a»: (cum) MENU CApl'r (3me cant wo yum—rue “Wm— u: 79. MULTIPLE-CHOICE QUESTIONS 1. If the direction of i is taken to be east and the direction of is taken to be north, which of the following vectors would be approximately in a southwestern direction? (A) (4km)T+A(7km)?A (B)(3mn)T:(5km)i A (C) —(7km)i (D) —(5km)i+(3km)j @—(5km)i—(4km)j 2. Which one of the following set of graphs of m(t),vx(t), and a$(t) belong together? x(t) mt) ax(t) :z:(t) mt) az(t) 2U) Mt) ax(t) (C) Opt ORt 0R 3”) Um”) at”) (D) 0% 0%t 0?): 1:05) mt) az(t) (E) ORt 0L::t {IF-t _-, 3. In which direction does the frictional P force on the mass m act in the situation . shown? (A) Parallel to and up the incline (B) Parallel to and down the incline (C) Perpendicular to the incline, directed outward (upward) D) Perpendicular to the incline, directed inward (downward) Either (A) or (B), depending on the magnitude of P 4. Which of the following statements about one-dimensional motion along the x-axis is false? ("Positive" refers to a vector in the + :1: direction and "negative" to a vector in the — x direction.) (A) If the acceleration of an object at t = to is nonzero, the velocity at t = to can be zero. (B) If the acceleration of an object at t = to is positive, the speed at t = to can be decreasing. . If the velocity of an object is constant, the acceleration is always zero. If the acceleration of an object at t = to is negative, the velocity at t = to must be negative. (E) If the position of an object is constant, the acceleration of the object is always zero. 5. If the magnitude of a force has the form k/r, where r is the distance from the origin, what are the proper SI units for k? (A) kg/s2 (B) kg - m/s2 ©kg - m2/s2 (D) kg (E) kg ~ m/s. 6. Near the earth‘s surface, a rock attached to a long rope is swinging in a circle in a vertical plane (like a pendulum). What is the direction of the net force on the rock when it o is at the bottom of its swing? (Neglect air - ,' resi nce.) Q up (B) down (C) left (D) right ( none, because the net force is zero. 7; Suppose that amass of 5.0 kg is subject to two forces: 1—51 = (7.5 N)? — (10 N)? and F2 = — (2.5 N) i. The acceleration of the object has a magnitude of approximately (A) 2.0 m/s2 2.2 m/s2 (C) 2.8 MP (D) 3.2 m/s2 (E) 4.0 m/s2 antities would _n_o_t_ be constant for an object moving 8. Which of the following physical qu g in uniform circular motion? Assume that the origin of the coordinate system is at the center of the circle. (A) its speed (B its acceleration “’ (C) its distance from the origin (E) the magnitude of the net force acting on it (D) its period of revolution 9. Which of the following statements is false? ( The acceleration of an object is always in the direction of the net force acting on it. B) The acceleration of an electric charge is always in the direction of the electric field acti g on it. t may be in a direction different than that of any of the (C) The acceleration of an objec forces acting on it; (D) If a force F, acting alone, same force, again acting alone, will pro on an object of mass greater than m. force due to the earth, the (E) If the net force on an object is just the gravitational magnitude of its acceleration will be greater near the earth's surface than far above the surface. a rider tends to slide towards the right side of the 10. When a car makes a sharp left turn, car. Which of the following explanations is correct? (A) The frictional force on the rider pushes the rider to the right. The frictional force on the rider causes the rider to slow down, leaving him behind. There is not enough frictional force on the rider for the rider to remain at a constant radial distance from the center of curvature of the motion. (D) The normal force of the seat back pushes the rider to the right. (E) None of the above. . . n ('1' on an object of mass m, the produces an acceleratio n of magnitude smaller than (a: duce an acceleratio ...
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This note was uploaded on 03/26/2008 for the course PHYS 221 taught by Professor Herrera-siklody during the Spring '08 term at Iowa State.

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exam1_1997s_sol - Name 0 Section P221/S97/Problem 1A [10...

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