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Unformatted text preview: December 2006 PHYS131 Version 1 ' .1 Final Examination VERSION # 1 Mechanics and Waves PHYS131 — All Sections
December 13, 2006 2 p.m.
Examiner: Prof. Roland Bennewitz Assoc Examiner: Prof. Sangyong Jeon INSTRUCTIONS: This is a CLOSED BOOK examination.
Only one double—sided CRIB SHEET permitted. Part of this examination (questions 19) is a MULTIPLE CHOICE examination.
0 The Examination Security Monitor Program detects pairs of students with unusually similar answer patterns on multiple—choice exams. Data generated by this program can
be used as admissible evidence, either to initiate or corroborate an investigation or a
charge of cheating under Section 16 of the Code of Student Conduct and Disciplinary
Procedures. MARK YOUR ANSWERS ON THE COMPUTER SHEET USING PENCIL ONLY. Make sure you have marked your version number on the computer sheet. Yours is Version 1. Answer questions 1014 into exam booklets. You are permitted TRANSLATION dictionaries ONLY.
Non—programmable calculators without graphic display permitted ONLY. This examination consists of 9 multiple choice questions and 5 worked problems on a total of
4 pages, including the cover page. THIS EXAMlNATION IS PRINTED ON BOTH SIDES OF THE PAPER You can keep the problem sheets if you want. PHYS— 1 31 Version 1 2 There are nine multiple choice questions. Only one answer per problem is correct. Each multiple choice problem
carries equal weight. The nine multiple choice problems count for 50% of the grade. 1) Two balls of equal size but different mass are thrown vertically into the air. They start at the same height with
the same velocity. Neglect air friction in this problem. Just to make sure: These balls do not collide. Which of
the following statements is true? (a) The ball with the higher mass reaches a larger maximum height. (b) The ball with the lower mass reaches a larger maximum height. (c) Both balls reach the same maximum height. (d) There is not enough information to decide. 2) Two balls of equal shape but different mass are thrown vertically into the air. They start at the same height
with the same velocity. This time, take air friction into account. Just to make sure: These balls do not collide.
Which of the following statements is true? (a) The ball with the higher mass reaches a larger maximum height. (b) The ball with the lower mass reaches a larger maximum height. (0) Both balls reach the same maximum height. (d) There is not enough information to decide, 3) The moment of inertia of a solid, homogeneous disk rotating around its center of mass is ICM=’/2MR2, where M is the mass of the disk and R is its radius. _.' ' ._ The disk is rolling over a surface like a wheel. What is the moment of inertia I p I " / '
for the disk with respect to the rotation around the contact point P between disk
and surface? (a) Ip is the same as ICM. (b) I p is two times ICM. (c) Ip is three times ICM. (d) 1,: is four times ICM. (6) None of the above. 4) Consider the motion of a particle in two dimensions
with constant acceleration. The initial velocity v, has a A magnitude of 1 m/s and the constant acceleration a has a y  magnitude of 1 m/sz. Their respective directions are
indicated in the ﬁgure. Which of the lines drawn in the figure resembles the path of the particle closest? x (a) Line A Vi (b) Line B D
(0) Line C (d) Line D a (e) Line E 5) A disk is spinning with angular velocity 0). A tangential force acts
on the rim of the disk. The direction of velocity and force are given
in the ﬁgure. With respect to the side of the disk which is visible in
the figure, which of the following statements is true: (a) The disk is spinning clockwise with decreasing speed. (b) The disk is spinning counterclockwise with increasing speed. (c) The disk is spinning clockwise with increasing speed. (d) The disk is spinning counterclockwise with decreasing speed. (e) Not enough information to decide which of the above statements is true. PHYS 13 1 Version 1 ' 3 6) A mediumsize car is traveling at a speed of 50 km/h. Which of the following values is the closest to the
kinetic energy of the car? (a) 1.5x10‘5 J (b) 1.5 J (c) 1.5x105 J (d) 15x1010 J (e) 1.5x1015 J 7) A rotating Disk A is placed rimonrim onto an identical Disk B which is initially at rest. Due to friction
forces, Disk A stops rotating with respect to Disk B after some time. The question is whether Disk B will start
rotating and if yes at what angular speed the two combined disks will rotate. Some more details: Disk B sits on a frictionless surface.
Initially, Disk B is at rest and Disk A is rotating with angular
speed 0) about the vertical axis through its center of mass.
Which of the following statements is true: (a) The angular momentum is conserved in this system and
Disk A and B will rotate with angular speed 0). (b) The angular momentum is conserved in this system and
Disk A and B will rotate with angular speed 03/2. (0) In order to calculate the angular speed of the combined
disks one needs to know the details of the frictional forces.
(d) Disk B will not start to rotate at all. (e) None of the above is true. 8) A cube of mass m rests on a horizontal surface.
The static coefﬁcient of friction is #3, the kinetic
coefficient of friction is ,uk. The cube is attached by a light spring with spring constant k to a wall.
By applying a horizontal force, the cube is moved
by a distance d away from its original position. Due to static friction, it rests in its new position.
Which of the following statements is true: (a) The work done by the force on the cube is ‘Vzkdz.
(b) The work done by the force on the cube is 1/2 kd2+mgukd. (c) The work done by the force on the cube is 1/2 kd2+ mgpkd + mgﬂs.
(d) The work done by the force on the cube is V2 kd2+ mg(,uk+,ux)d.
(6) None of the above statements is true. 9) The amplitude of a transversal mechanical wave is doubled, with no other changes made to the wave. As a
results of this doubling, which of the following statements is correct? (a) The speed of the wave changes. (b) The frequency of the wave changes. (c) The maximum transverse speed of an element of the medium changes.
(d) All of (a)(c) are true. (e) None of (a)(c) is true. PHYS—131 Version 1 4 There are ﬁve worked problems. Each worked problem carries equal weight. The five worked problems count
for 50% of the grade. Write your complete solution into the exam booklet. Write readable! If we cannot read
your answer, we cannot give you credit! 10) A cube with mass m=1.00 kg is resting
on an inclined plane which forms an angle 0
= 10.0” with the horizontal. A static friction
force prevents it from sliding down the
incline. (a) Draw the freebody diagram for the cube. .  . __ _ (b) Calculate the static friction force acting L "I; ____________________ __ J; _§';___'__:“_'_'__."__'_‘._._ _ ‘_ __ _.._._ _._ _ ____
on the cube. Your result must be a vector, ' i " ' ' ' ' ' '
write down its components. You must use the coordinate system indicated in the figure. Use g=9.80 m/s2 for your calculation. 11) The radius of the Earth is RE=6.37x106 m. The gravitational constant is G=6.67><10'“ Nmz/kgz. The free—fall
acceleration at the surface of the Earth is g=9.80 m/sz. Using these three numbers, ﬁnd the average density of the Earth. (The volume V of a sphere with radius r is given by V=4/3 Irrj) 12) Two bodies with a mass of 2.00 kg and 3.00 kg are connected by a light string. They move on a horizontal frictionless surface. A horizontal force F of F
5.00 N is applied to the 3.00kg body. (a) What is the acceleration of the two bodies? (b) What is the tension in the string? 13) The coefﬁcient of kinetic friction between the 3.00 kg block and the
surface in the figure is 0.400. The system starts from rest. What is the speed
of the 5.00kg ball when it has fallen 1.70 m? You can neglect the moment
of inertia of the pulley. You should consider using energy conservation in
your solution. 14) A pendulum is made from a mass m1=1.00 kg suspended in a string of l=1.00 m
length. Initially, the mass m; is at rest. A second mass m2=1.00 kg is hitting ml with
a speed of v2=1.00 m/s. At the instant of the collision (t=0) there is no velocity
component in vertical direction. The collision is perfectly inelastic; the two masses
stick together. The resulting oscillatory motion of the pendulum can be described
as 6(t)=00sin(at), where 0 is the angle the pendulum forms with the vertical.
Calculate wand 00. You can treat the masses as particles. Use g=9.80 m/s2. ...
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