exam01_sol_f08 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 Fall Term 2008 Exam 1 Solution Problem 1: (25 points) Concept Questions: Circle the correct answer for the following five questions. A. (5 points): During a race on a straight track, a person moves with constant acceleration, then continues at constant velocity, then experiences at a constant deceleration until coming to a stop. Which of the following graphs best represents the position as a function of time ? (1) (2) (3) (4) None of the above. (5) (6) Solution: (5).
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2 B. (5 points): Starting at the same instant, two objects A and B are pushed on a frictionless surface from a starting line to a finish line with equal constant forces. Object B is four times as massive as object A. Both objects are initially at rest. 1. Object A has four times the acceleration as object B and reaches the finish line in half the time as object B. 2. Object B has four times the acceleration as object A and reaches the finish line in half the time as object A. 3. Both objects reach the finish line at the same time with the same speed. 4. Object A has four times the acceleration as object B and reaches the finish line in one quarter the time as object B. 5. Object B has four times the acceleration as object A and reaches the finish line in one quarter the time as object A. 6. Object A has twice the acceleration as object B and reaches the finish line in half the time as object B. 7. Object B has twice the acceleration as object A and reaches the finish line in half the time as object A. 8. Not enough information is given to decide. Solution (1). The force acting on each object is the same. Object A has one quarter the mass of object B so it has four times the acceleration. Both objects travels the same distance 2 (1/ 2) da t = , so the time to reach the finish line is 2/ td a = . Since object A has four time the acceleration of object B it reaches the finish line in half the time that it takes object B.
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3 C. (5 points): A skier of mass M slides down a ramp shaped as a circle of radius R . At the end point of the ramp just before the skier is in the air, the magnitude of the normal force exerted by the ramp on the skier is N . The gravitational constant is g . 1) The magnitude of the normal force N greater than Mg . 2) The magnitude of the normal force N equal to Mg . 3) The magnitude of the normal force N less than Mg . 4) The magnitude of the normal force N can be greater than, equal to, or less than Mg depending on the speed of the skier. Solution (1): The forces on the skier on shown in the figure below. Since the skier is still undergoing circular motion at the instant just before leaving the track, the skier is accelerating upwards. If the skier has speed v at that instant then applying Newton’s Second Law to the skier yields 2 / NM gM vR −= (1.1) We can solve this for the magnitude of the normal force 2 / =+ . (1.2) Therefore the magnitude of the normal force is greater than the magnitude of the gravitational force at the instant just before the skier leaves the track.
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4 D. (5 points):
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This note was uploaded on 10/15/2011 for the course PHYSICS 0207239 taught by Professor Mamar during the Spring '09 term at Jordan University of Science & Tech.

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exam01_sol_f08 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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