Scalar Product - General Physics - Past Paper, Exams of Physics

Download Scalar Product - General Physics - Past Paper and more Exams Physics in PDF only on Docsity! AJM:3/25/04 Score /100 Physics 131 Final Exam Winter 2004 Name You may use two sheets of notes (8-1/2 x 11, both sides) and a standard calculator. No communication or photo- graphic devices. No hats. Work the problems on separate sheets of blank paper and staple this sheet to the front. Read each problem carefully and be sure to pay attention to any hints that are provided. The credit you receive on each problem will depend at least as much on how you get your answer as on what answer you get. There is no need to be “wordy” as I ask you to be on homework, but you must show your work or give at least a brief explanation for every answer. I give no credit for unsupported answers. I give partial credit for partially correct solutions, but only when I can figure out what you are doing, so be as clear as possible. Make certain that all numerical answers are given with a reasonable number of significant digits (when in doubt, three is usually a good compromise) and that you have included appropriate and simplified units. Check your answers for physical reasonableness whenever possible; I do deduct a small number of points for ridiculous answers that go uncommented upon. In every problem you may use g = 10.0 N/kg in order to make the computations simpler. 1. Consider the two vectors € A = 3.0 ˆ x − 2.0 ˆ y ( ) m and € B = 4.0 ˆ y −1.0ˆ z ( ) N . a) [4 pts] Find their scalar product. b) [4 pts] Find their vector product. c) [4 pts] Find the angle between them. 2. A 300 gram hockey puck is subject to 75 mN of frictional force as it glides across the ice. a) [4 pts] What is the magnitude of the acceleration of the hockey puck. The puck is given an initial speed of 25 m/s after which it glides the full length of a 50 m rink. b) [8 pts] How fast is it moving when it reaches the other end of the rink? [Hint: Use the method!] 3. A ball is tethered to a vertical pole by two ropes as shown at right. It moves around the pole at a constant speed constrained by the ropes to move in a circular path. The tension in the shorter (horizontal) rope is equal to the ball’s weight. a) [6 pts] What is the tension in the longer rope? Give your answer in terms of the ball’s weight. [Hint: Use the method!] b) [9 pts] If the length of the shorter rope is 1.5 m, how long does the ball take to make one revolution? [Hint: Find it’s speed and the circumference of its circular path!] 4. Two particles approach each other from opposite directions as shown top right. Their masses and speeds are as shown (in terms of m and v which may be considered to be “given.”) They suffer a glancing collision that deflects the lighter particle counterclockwise through an angle of 90 degrees and leaves it moving with the speed shown below right. a) [10 pts] Find the velocity of the heavier particle after the collision. Give its speed in terms of v and its direction in terms of the angle of deflection from its original direction as I did (above, in italics) for the lighter particle. b) [5 pts] Was this an elastic collision? Explain clearly. 5. [12 pts] A 5.0 kg disk is or radius 15 cm is free to rotate about its axis, which is held fixed and horizontal. A string is wrapped around the perimeter and a 1.0 kg block is attached to its free end. What is the linear acceleration of the block when it is released? [Hint: Consider the forces on the block and the torque on the disk. EXTRA CREDIT [5 pts] At any later time, what is the ratio of the kinetic energy of the disk to that of the block? (over) L L Pole Ropes m2m v 3v Before 2v ? After