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Unformatted text preview: ME 270  Fall 2004 SOLUTION
Final Exam
PROBLEM NO. 1 Given: Pin P travels on a wire whose shape is given by y = 0.5x2. Pin P is also constrained to move within a slot in guide B where the guide has a constant
speed of v3 =10ft/sec to the right. Find: At the position shown, x = 2 ft. For
this position: y
a) Find the velocity 3,; and Wire, y = 0.5x? acceleration Q}; of P. Write your answers as vectors in terms of
Cartesian coordinates. (8 points) b) Sketch 1P and gp in the ﬁgure.
(2 points)
c) Sketch the unit tangent and unit normal vectors, g, and en, for the path of P in the ﬁgure. (2
points) d) Determine the rate of change of
Speed of P. {8 points) y = 0.5x2 = 0.5(2)2 = 2ft
y = xx =(2)(10)= 20ft/sec y = xx+ xx: (10)2 +0: lOOft/se02 Therefore, KP =xi+yi=(10i+201)ft/sec gp = :m ya: (100th/sec2 3113:101_‘+201=v,pet => 10'+20‘
e =£ﬂ=_£___l=0.447§+0.8941 v'P = gp 0e, = (1001)  (0.447g+ 0.8941) = 89.4 ft/secz ME 270  Fall 2004 SOLUTION
Final Exam
PROBLEM N0. 2 Given: Particle A, having a mass of 5 kg, is constrained to move within a smooth slot
in an arm. The arm is rotating counterclockwise at a constant rate of
a) = 8 rad /sec about point 0 within a horizontal plane. A constant force F A = 150 newtons acts on particle A in the outward radial direction. The radial
distance from O to A is given by the distance r shown in the figure. Find: For this problem, do the following.
a) Complete the free body diagram (FBD) of A above. Show the polar
unit vectors e, and ea in your FBD. (5 points)
b) Write down Newton’s second law for the particle in terms of polar
coordinates. (4 points)
c) If r = 4 m / sec when r = 0.2 meters, determine the value of r when
r = 0.6 meters. (6poz'nts) d) Determine the contact force F S of the slot on particle A when
r = 0.6 meters. (5 points) 2F, = FA =m(r—r92)
ZFQ =FS =m(ré+2r9) Using first equation, r=F—A+r92 =>
m
.di
r——— =>
dr 1(r2 — r‘oz) = %(r—— r0)+ $9202 — r02) => f: fg+2F—A(r—r0)+92(r2 —r02)
V m = (4)2 + (8%(06—02) + (8)2(0.62 —0.22) = 7.78 m/sec Using second equation:
F5 = m(ré+ 2%)) =<s>[o+<2)<7.78><8>] = 622N ME 270  Fall 2004 Name
Final Exam
PROBLEM NO. 3 Instructor Given: A tank is divided into two sections by a 1m x 1m square gate with a hinge at
A. The right side of the tank is ﬁlled with water ( pW = 1000 kg/m3) and the left side is ﬁlled with methanol (pM = 789 kg/m3) in such a way that the ﬂuid height, H, in each tank is the same and increases at a rate 1¥= 0.1 m/minute. A
moment M is applied to the gate to prevent mixing of the two ﬂuids. gate Methanol Water
—.._> 4—
Find: Determine the moment M needed to prevent mixing of the ﬂuids at 5 minutes after the start of the ﬁlling of empty tanks. Assume that there is no friction
between the bottom of the gate and the tank bottom. ME 270  Fall 2004 Name
Final Exam
PROBLEM NO. 4 Instructor Given: A 100 lb force is applied to the point A on link ACD of the mechanism
shown below. Joints C and D are pinned connections. Assume a
smooth surface at B. You will be asked to find the force F required to
maintain equilibrium. 7 y D C
o—
100lb
4ft
60°
A
B 2ft
7 / V / F 2ft
5ft 4ft l2ft‘3ft Find: For this problem, do the following:
a) Draw free body diagram of the whole structure and of member BC. Ignore the weight of the links. (6 points) \ b) Are there any twoforce members on the structure? Simply answer as
Yes or No. (2 points)
c) Find the force F for equilibrium. (12 points) PLEASE START YOUR WORK FOR PART c) ON THE NEXT PAGE. ME 270  Fall 2004 Name
Final Exam
PROBLEM NO. 5 Instructor Part a) — 5 points
State Newton’s three laws in words as succinctly as possible. I. II. III. ME 270  Fall 2004 Name
Final Exam PROBLEM NO. 5 (cont.) Instructor Part b) — 5 points For the cable system shown below, the tension in cable BB is known to be 200 1b. Write the force exerted on point E by cable EB as a vector in terms of the Cartesian components
corresponding to the coordinate system provided. (6, 1.4. 1.2) m \t (2.2.(J.—l) m
D A (2.2.0.1)m ll
5"
A ME 270  Fall 2004 Name
Final Exam PROBLEM NO. 5 (cont.) Instructor Part c) — 5 points In many cowboy ﬁlms, one often sees the cowboy get off his horse and wrap a rope
around a horizontal hitching rack to keep the horse from wandering away. For the
purposes of this problem, assume that the cowboy wraps the rope 3+ times around the
hitching rack and then lets the free end of the rope hang down. What is the maximum
force that the horse can pull on the rope does not slip? Assume that the free end of the
rope has a weight of 0.3 lbs., 0 = 45° and ,uS = 0.4, where ,uS is the coefﬁcient of static
friction between the rope and the hitching rack. Do you think this force is enough to
prevent the horse from wandering away? To Horse / hitching rack \ free end of rope ME 270  Fall 2004 Name
Final Exam
PROBLEM N0. 5 (cont.) Instructor Part (I) — 5 points Consider the stamping mechanism shown below. Identify by name the twoforce
members in this mechanism. ...
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