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Unformatted text preview: ME 274: Basic Mechanics 11 January 19, 2011
Spring 2011 Fundamentals Exam
January 19, 2011 Instructions: 0 You have 50 minutes to complete this exam. 0 This is a closedbook, closed—notes exam. 0 The exam has 13 questions. Problems 1—8 are worth 4 points maximum. Problems 912 are
worth 2 points maximum. Problem 13 is worth 8 points maximum. 0 Partial credit is not given on any problem for which you have made a fundamental error. 0 You are allowed to use a calculator during the exam. 0 Usage of mobile phones and other electronic communication devices is NOT permitted during
the exam. Equations: 2 vét v2 . . = rbét + "én
= RéR + Raég 27=gbi+y3 a (a _ 392) a + (my + 2129) a, Problem Score Fundamentals Exam (1a) Page 1 of 8 ME 274: Basic Mechanics II Spring 2011 For Problems 1—2 use the following vectors (i and 3: a: <ﬁi—V5}+3l§)ft, 6 ll Problem 1 (4 pts)
What is the scalar projection of (‘1’ onto the direction of b? a 2.
lbl A A A z "(513 r3k> W
 (ammo) _ 3&5:
—' 5 a 5 5
Problem 2 (4 pts)
What is the scalar projection of 1; onto the direction of ('1'?
» a.
b ’ m A
A 4
= (Wail tail “1% +30 January 197 2011 (4%+3I%) ft
Answer: r
35— + 1; ¥‘+ l Answer: Fundamentals Exam (1a) Page 2 of 8 ME 274: Basic Mechanics 11 January 19, 2011
Spring 2011 Problem 3 (4 pts) If = ex + §x3, find i when (I? = 0, i: = 2, y' = 2 and g = 1. ac and y have units of meters and
time is in seconds. =2 l=<l+z©))(z)z+(l+0‘>§£
31> 1:44—5695 5l=‘3m/51 Problem 4 (4 pts) A particle P moves along a straight line with a = 3552 + 4933 ft/s2. If P has an initial speed of 3
ft/s, ﬁnd the speed of P after the particle has traveled 1 ft. 7— 3 Answer:
a ; 3x * Ll)“ :
a’u ’3 ‘Hr/j z z
, V ,V0
3? IIBZW’XVX"? L
0
Z 1.
3 L4 \ :‘L’£__
:9 X +X o 2, 1—— Fundamentals Exam (1a) Page 3 of 8 ME 274: Basic Mechanics 11 January 197 2011
Spring 2011 Problem 5 (4 pts)
The acceleration of particle P is given by d = —52' + 123' m/s2. Express the vector 55 in the path coordinates shown in the ﬁgure (not to scale). Problem 6 (4 pts)
The velocity of a particle moving in the plane is given by 17 2 31' m/s. If the acceleration of the particle is known to be (i = 4% + 55' m/s2, find the particle’s rate of change of speed. {/7} = 2" Answer:
a = 414+ 5'3
'3 /\
é :— .y'— : ’l
t IW Fundamentals Exam (1a) Page 4 of 8 ME 274: Basic Mechanics 11 January 197 2011
Spring 2011 Problem 7 (4 pts) A particle P moves along a path described by 7" = cos 20 In and 9 = 2 rad/s, where 9 is constant. Find the acceleration vector of P in polar coordinates corresponding to the instant when 9 = r: cos 29
é“ : ‘ri: ~Llcaszee'Z—Zsz‘nzee « “NW/JON lam/51b
a"(l*‘rézlé\r+(z€~é+ré)é\¢9
= [WC—007$? 2r + [Hex—2) + (4%)]ng : ZOM/szér Problem 8 (4 pts)
A force F = 12' + 29' kN acts at point P. The position of point P relative to point 0 in the x—y plane
is known to be: 7” = —O.52' + j In. Find the moment about point 0 due to force F. F. A A A Answer: A
2 a 73‘ x )}*Z‘ ~2me
( J) ( J) Fundamentals Exam (1a) Page 5 of 8 ME 274: Basic Mechanics II
Spring 2011 January 19, 2011 ___—__——_——.———_—————_—— Problem 9 (2 pts)
The dot product of two vectors (‘1’ = (2332' + ay j and b = bzi + by} is given by: (g) None of the above. Problem 10 (2 pts) #
The magnitude of the vector b = bmi + by j is accurately represented by: (a) EI=W
(b) lzlbml'l‘lbyl (C) 5l=lbx+by (d) 13l= lbm+byl
(e) 61:53; (f) bl: 13.17 (g) None of the above. Fundamentals Exam (1a) Page 6 of 8 ME 274: Basic Mechanics 11 January 19, 2011
Spring 2011 Problem 11 (2 pts) A force F acts in the (is—y plane at point P. Which answer below most accurately describes the
moment created by the force about point 0: (@ mb==dm1snet w)Mb=aﬁsma_nk Problem 12 (2 pts) A stepped, homogeneous disk having weight W and resting on a rough incline is held in place by a cable, as shown. Draw a free body diagram of the disk. The friction force on the disk at contact
point C: a) acts in a direction corres ondin to u the incline.
(b) acts in a direction corresponding to down the incline.
(c) is zero. (d) More information is needed about the problem in order to determine the direction of this
friction force. T
"'3 A/\F‘ Fundamentals Exam (1a) Page 7 of 8 ME 274: Basic Mechanics 11 January 19, 2011
Spring 2011 Problem 13 (8 pts) Blocks A (mass m) and B (mass 2m) are connected by the cable—pulley system shown below. Assume all surfaces to be smooth. Complete the four free body diagrams shown in the box below
for this system. Fundamentals Exam (1a) Page 8 of 8 ...
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