PHYSICS 218 Exam 3 FALL, 2009 Do not fill out the information below until instructed to do so! Name:__________________________________ Signature:_______________________________ Student ID:______________________________ E-mail:__________________________________ Section Number: _________________________ • You have the full class period to complete the exam. • Formulae are provided. You may NOT use any other formula sheet. • When calculating numerical values, be sure to keep track of units. • You may use blank pages provided with this packet as scratch paper or come up front to get more. • Be sure to put a box around your final answers and clearly indicate your work to your grader. • All work must be shown to get credit for the answer marked. If the answer marked does not obviously follow from the shown work, even if the answer is correct, you will not get credit for the answer. • Clearly erase any unwanted marks. No credit will be given if we can’t figure out which answer you are choosing, or which answer you want us to consider. • Partial credit can be given only if your work is clearly explained and labeled. Put your initials here after reading the above instructions: ________SCORE Part 1 (25) ___________ Part 2 (25) ___________ Part 3 (25) ___________ Part 4 (25) ___________ Total (100)___________Problem 1 (25 points): Short Questions In the following questions you should show your work, just circling your answer will not result in any credit. 1 (2pts) A block of mass m, moving on a frictionless surface with a speed vi, makes a perfectly elastic collision with another block of unknown mass M at rest (see Figure below). After the collision, the block of mass m recoils with a speed of vf. From this information, the mass M should be equal to (Hint: a2-b2=(a+b)*(a-b)): A M = 2*m*vi/(vi-vf) B M = m*(vi+vf)/(vi-vf) C M = m*(vi-vf)/(vi+vf) D M = 2*m*vf/(vi+vf) E M = m*vi/(vi+vf) 2 (4pts) A high-school pitcher is employing a ballistic pendulum to determine the speed of his fastball. A lump of clay of mass M is suspended from a cord of length l. When the pitcher throws his fastball aimed at the clay, the ball becomes embedded in the clay and the two swing up to a maximum height of h. The mass of the baseball is m. Find the speed of the pitch. A mMlhg )(2 + B mmMlhg−+ )(2 C MmMgh+2 D mmMgh+2 E MmMlhg−+ )(23 (4pts) A very rigid ball of mass M is hanging from a long but very light flexible wire when it is struck by a stone of mass m traveling horizontally to the right at speed vi. The stone rebounds to the left with a speed of vf m/s, and the ball swings to a maximum height h above its original level. The value of h is closest to: A h=gvvMmfi2)(2+⎟⎠⎞⎜⎝⎛ B h=gvvMmfi2)(2−⎟⎠⎞⎜⎝⎛ C h=gvvMmfi2)(22+⎟⎠⎞⎜⎝⎛ D h=gvvMmfi2)(22−⎟⎠⎞⎜⎝⎛ E h=gvvMmfi2)(2−⎟⎠⎞⎜⎝⎛ 4 (3pts) A light triangular plate OAB is in a horizontal plane (see Figure below). Three forces, F1 = 3 N, F2 = 1 N, and F3 = 9 N, act on the plate, which is pivoted about a vertical axes through point O. The moment arm of force F1 about the axis through point O is closest to (Hint: sin 300=0.5, cos300=√3/2, sin 450= cos 450 =√2/2): A 0.9*√3 B 0.9 C 0.6*√2 D 0.6*√2 E 1.85 (4pts) A uniform solid cylindrical log begins rolling without slipping down a ramp that rises θ=300 above the horizontal. After it has rolled distance d=2m along the ramp, the magnitude of its linear acceleration is closest to: A 9.8 m/s2 B 6.6 m/s2 C 5.7 m/s2 D 3.3 m/s2 E 2.1 m/s2 Hints: sin 300=0.5, cos300=√3/2, g=9.8 m/s2, Moment of inertia of a uniform filled cylinder around its center is I=1/2mR2, where R is the radius and m is the mass 6 (2pts) Which of the following is an accurate statement? A If the speed of a particle is constant, then the angular momentum of the particle about any specific origin must also be constant. B The angular momentum of a moving particle depends on the specific origin with respect to which the angular momentum is calculated. C If the torque acting on a particle is zero about an arbitrary origin, then the angular momentum of the particle is also zero about that origin. D A particle moving in a straight line with constant speed necessarily has zero angular momentum. E Consider a planet moving in a circular orbit about a star. Even if the planet is spinning it is not possible for its total angular momentum to be zero. 7 (2pts) When is the angular momentum of a system constant? A when the total kinetic energy is constant B when no torque acts on the system C when the linear momentum and the energy are constant D when the moment of inertia is constant E when no net external force acts on the system8 (2 pts) A metal bar is hanging from a hook when it is struck by a ball that is moving horizontally (see Figure below). The ball is covered with glue, so it sticks to the bar. During this collision: A Both the angular momentum of the system (ball and bar) and its kinetic energy are conserved. B Both the linear momentum and the angular momentum of the system (ball and bar) are conserved. C The angular momentum of the system (ball and bar) is conserved about the hook because only gravity is acting on the system. D The angular momentum of the system (ball and bar) is not conserved because the hook exerts a force on the bar. E The angular momentum of the system (ball and bar) is conserved about the hook because neither the hook nor gravity exerts any torque on this system about the hook. 9 (2 pts) When is the angular momentum of a system constant? A when the total kinetic energy is constant B when no torque acts on the system C when the linear momentum and the energy are constant D when the moment of inertia is constant E when no net external force acts on the systemProblem 2 (25 points): A ball of mass M, hanging from the ceiling by a light wire of length l, is struck in an elastic collision by another ball of mass m moving horizontally with speed v just before the collision. Find the tension in the wire just after the collision.Problem 3 (25 points): A uniform hollow disk (inner radius r and outer radius R) has two pieces of thin light wire wrapped around its outer rim and is supported from the ceiling (the figure below). Suddenly one of the wires breaks, and the remaining wire does not slip as the disk rolls down.
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