final_exam_practice_sols

final_exam_practice_sols - MASSACHUSETTS INSTITUTE OF...

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 Fall Term 2009 Practice Problems Final Exam: Solutions Part One: Concept Questions Problem 1: A small cylinder rests on a circular turntable, rotating at a constant speed as illustrated in the diagram below. Which of the vectors 1-5 below best describes the velocity, acceleration and net force acting on the cylinder at the point indicated in the diagram? Answer: 4: (Turntables went out when Jerry Garcia did, but that’s not part of the problem.) The velocity is to the right in the figure; the acceleration and the force are inward, down in the figure. Problem 2: A hollow cylinder starts from rest and rolls without slipping down an incline. Which of the following best describes the force of friction? The magnitude of the normal force is N .
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2 1. The force of friction is kinetic friction, with k f N μ = . 2. The force of friction is static friction, with s f N = . 3. The force of friction is static friction, with f equal to the force necessary to prevent slipping, up to a maximum of max s f N = . 4. The friction is zero because the cylinder rolls without slipping. Answer: 3. For rolling without slipping, the friction force cannot be kinetic. The static friction force must be less than the product of the coefficient of static friction s and the magnitude N of the normal force. Problem 3: The figure below depicts the paths of two colliding steel balls, A and B . Which of the arrows 1-5 best represents the impulse applied to ball B by ball A during the collision? Answer: 1; Ball B has changed its momentum in the upward direction in the figure, and as far as the figure can show, there is no change in its horizontal (rightward) velocity. Problem 4: An object is dropped to the surface of the earth from a height of 10m . Which of the following sketches best represents the kinetic energy of the object as a function of time as it approaches the earth if friction can be neglected? Take 0 t = as the time when the object is dropped.
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3 1. a 2. b 3. c 4. d 5. e Answer: 3 c . The object manifestly has no kinetic energy at 0 t = , and increases at a rate proportional to the square of the time t . Problem 5: A bicycle wheel is initially spinning with non-zero angular speed about the center of mass. The wheel is lowered to the ground without bouncing. As soon as the wheel touches the level ground, the wheel starts to accelerate forward until it begins to roll without slipping. In the figure below, S denotes a point on the ground along the line of contact between the wheel and the surface. From the moment the wheel touches the ground until it just begins to roll without slipping, the angular momentum is 1. constant about the wheel’s center of mass. 2. constant about the point S . 3. constant about both the wheel’s center of mass and the point S .
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This note was uploaded on 04/13/2011 for the course PHYSICS 8.01 taught by Professor Guth during the Fall '09 term at MIT.

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final_exam_practice_sols - MASSACHUSETTS INSTITUTE OF...

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