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Unformatted text preview: ME 270 Final Examination Name
May 6, 2004 (Print) (Last) (First) PROBLEM #1 120 points) The following subproblems labeled 1(a) to 1(e) are worth either 4 points for the correct answer or zero points for the wrong answer (no partial credit, no matter how trivial the
mistake). 1(3) (4 points, no partial credit) In your Own words. state each of Newton's three laws of motion. Be sure to write legibly.
Unreadable deﬁnitions will be marked wrong. 1(b) (4 points, no partial credit) For the system sh0wn, calculate the equivalent moment about point 0 due to the loading
shown. Do n_ot consider the reactions at the wall (point 0). 1 (c) (4 points, no partial credit) For the truss shown. identify all zeroforce members. ZeroForce Members = 1 (d) (4 points, no partial credit) For frame ABCD (shown), complete the overall and individual freebody diagrams shown
below with any missing reactions. Be sure to label all of your reactions. (d) 1 (e) (4 points, no partial credit) The tensile force T is applied to the free end of a cable that is wrapped around the horizontal
binding post (A) for one complete revolution and then attached to the 60 lb crate. The coefﬁcient of static friction between the post and the cable is 0.3. Determine the minimum tension (T) for
which the crate will not decend. ..
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.
C
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. —— ill!!!l.liiiiillll .
u—u l (e) (4 points, no partial credit) Bar AB is loaded as shown and is in static equilibrium. Determine the magnitude of the reaction
force at roller support B and indicate whether this reaction is to the right or to the left. (circle one) ME 270 Final Examination Name
August 5, 2004 (Print) (Last) (First) PROBLEM #2 (20 mints) Given: An 8ftlong boom is held by a ballandsocket joint at C and by two cables at AD and
BE. Find:
(3 pts) (a) Draw a complete free body diagram for boom ABC. (4 pts) (b) Write vector expressions for forces T35 and TAD in terms of their unknown
magnitudes and their known unit vectors. (10 pts) (c) Determine the magnitude of the tensions in cables BE and AD. (3 pts) (d) Determine the magnitude of the reaction force in the xdirection at the balland
socket joint at C (Le. Cx ). 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 H 0.1 III/minute. A
moment M is applied to the gate to prevent mixing of the two fluids. Methanol Find: Determine the momth needed to prevent mixing of the fluids at 5 minutes aﬁer the start of the ﬁlling of empty tanks. Assume that there is no friction
between the bottom ofthe 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. y D C
lo—
100 lb
4 fl
60°
A
B 2 ft
2 ft 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) D C C
A
B B
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) ME 270  Fall 2004 Name
Final Exam PROBLEM N0. 5 Instructor Part a)  5 points State Newton’s three laws in words as succinctly as possible.
I. 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 EB is known to be 200 lb. Write
the force exerted on point E by cable EB mm in terms of the Cartesian components
corresponding to the coordinate system provided. (‘4. LG)!“ ME 270  Fall 2004 Name
Final Exam PROBLEM N0. 5 (cont) Instructor Part c) — 5 pain“ 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 [ls 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 ME 270  Fall 2004 Name
Final Exam PROBLEM NO. 5 (cont.) Instructor Part d) — 5 points Consider the stamping mechanism shown below. Identify by name the twoforce
members in this mechanism. ME 270 Final Examination Name
May 6, 2005 (Prim) (Last) (First) PROBLEM #1 (20 points) The following subproblems labeled 1(a) to l(e) are worth either 4 points for the correct answer or zero points for the wrong answer (no partial credit, no matter how trivial the
mistake). 1(a) (4 points, no partial credit) Please determine the reaction force due the water on the vertical face of a wall, also give
its application point with respect to the origin 0. Assume the speciﬁc weight of water is
7wmr=624 113/113 TM an.“ s v.9; +4. ck. 1—.  on. I y T 3.00 ft water depth 1(b) (4 points, no partial credit) Determine the maximum speed a driver can proceed at the top of a hill (with radius
p = 30 it) without the vehicle leaving the ground (going airborne). ME 270 Final Examination Name
May 6, 2005 (Print) (Last) (First) PROBLEM #2 (20 points) GIVEN: Tmss A — L (shown below) is supported by a pin support at joint A and a roller support at joint I. The truss is loaded with three forces as shown. (Remember 1 kip = 1000
lbs.). FIND: For the structure shown below, please determine:
(2 pts) (a) The zeroforce members in the truss that can be determined by inspection.
(6 pts) (b) The magnitudes of the reactions at point A and point I. (12 pts) (c) The magnitudes of the forces of members EF, PK and JK and state whether they are
in tension or compression. 1O kips Name ME 270  Summer 2005
Final Exam
PROBLEM N0. 1 Statics  short answer. Each part of this problem is worth 5 points. Please answer them as
succinctly as possible. IA. Resolve the distributed load into a single force (located at the appropriate point) and draw a
complete free body diagram of the cantilevered beam. Neglect the weight of the beam. 200 N/m Y 18. Complete the following table by recording the maximum number of scalar equations that can
be generated for static equilibrium in the following cases: Model S stem ——
Riid Bod —— Name IC. The Kursk was one of the larger submarines in the Russian Navy. When submerged it
displaced l8.300 tons of water. It was approximately [54 m long. 18.2 m tall. and L) m wide and
was powered by 2 nuclearpowered turbines. The turbines produce a combined thrust of 27 ki\'.
If the turbines are a distance d = 9.1 m above the base of the submarine. the center of mass is 3 m
above the base of the submarine. and L = 90 m. calculate the moment produced by the turbines
relative to the submarine‘s center of mass. 3:: 1D. In 2002. there was a group touring the Aquarium of the Americas in New Orleans. LA and
they were allowed to walk on the catwalk that the staff used to feed the sharks. Unfortunately the
catwalk failed and dumped the guests into the shark tank. Nobody was injured. but they were
quite frightened. Below is a new design for the catwalk. Please do the following: First. calculate the centroid of the catwalk relative to the point. 0. Second. assume that the catwalk is going to be a uniform thickness of 2 em. but will be
manufactured out of two different materials. If the ramp of the catwalk (in white) is made out of
stainless steel. and the platform (in gray) is made of a fiber reinforced composite material. what
is the center of mass relative to the point. 0‘? The density of the steel is p~ = 7.530 kg/‘m; and the
density of the composite material is p. = 1.400 kg/ni‘. Name ME 270  Summer 2005
Final Exam
PROBLEM NO. 2 Given: A toggle clamp holds the workpiece, H, in place on the table. A downward force of
50 N is applied to the handle at G. Find: Calculate the clamping force at point E. Make sure you include appropriate free body
diagrams. Name ME 270  Fall 2005
Final Exam
PROBLEM NO. 1 Given: The end of a fresh water channel consists of an Lshaped solid plate ABC which is
pinned at B and is 1 ft. wide (i.e. 1 foot out of the paper). There is a roller support at point A. The
speciﬁc weight of the water is y = p, = 62.4 lb/fr’. C Find: a) Determine the equivalent point loads that the water exerts on both surfaces (BC and AB) of
the plate. (6 points) b) Using the ﬁgure provided, draw the freebody diagram of gate ABC, denote the coordinate
axes and clearly indicate the proper location for the equivalent loading. Neglect the weight of
the gate and neglect the thickness of the gate. (5 points) c) Determine the reactions at A and B. (9 points) Name ME 270  Fall 2005
Final Exam
PROBLEM NO. 2 Statics  short answer. Each part of this problem is worth 5 points. Please answer them as
succinctly as possible. 2A. If the coefﬁcient of friction between the legs of the crate and the ground is 0.7, what force,
F, is required to make the crate move? Does it tip or slip? (5 points) I—2ft.—I Sft. F: Tip or Slip? (Circle One) Name 28. Determine the angle between the position vectors AB and AC. (5 points) Name 2C. Calculate the ycomponent of the centroid for the vertical stabilizer shown below. (5 points) ycenumd = 2D. If the PCI card weighs 0.75 lb. and the weight acts at the point indicated, calculate the moment it exerts about the origin (0). Write it in vector form. (5 points)
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This note was uploaded on 12/21/2011 for the course ME 270 taught by Professor Murphy during the Fall '08 term at Purdue UniversityWest Lafayette.
 Fall '08
 MURPHY

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