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Unformatted text preview: ME 270
PROBLEM #1 EM»? 1% 1‘: Y‘J Exams Given: The lever ABC is pinsupported at A. Link ED
is pinconnected at B and at D. The weight of the
members can be neglected. Find: (a) The free body diagrams for the lever and the
link.
(b) The force vector FA acting on the lever at A. (c) The force vector is]; acting on the link at D. b) a; 5337+ 6835‘ N a) g: 9337“— 9335‘ PROBLEM #2 Given: The crate has a weight mg = 200 lb. Find: (a) For h = 4 ft and us 2 0.4, determine the minimum horizontal force P required
to cause impending motion of the crate. ‘
Will the impending motion be slipping or tipping? Justify your answer. (b) What would have to be h so that the
crate is in impending slipping an_d
tipping at the same force F? What is
this force? a) at: [0015 l 80/6 { b) h: 535+ PROBLEM #3 (20 points! Given: An automobile follows a circular track at a constant speed v = 20 m/s.
Find: For the instantaneous position shown in the ﬁgure, obtain the following: (a) The velocity and acceleration vectors V and i in path coordinates. (b) The velocity and acceleration vectors V and u in cylindrical coordinates with origin
at 0. (c) The values of R, R, éand i3. Reminder: Deﬁne the unit vectors you are using in the ﬁgure. Show all your work. [2,: —o.2.83 AMI/52'
‘9: 42.010 moi/s
é: O rad/52— PROBLEM #4 120 points: Given: The weights of blocks A and B are WA = 15 lb and W3 = 20 lb. At time t = 0 they are at
rest. All surfaces are well lubricated (zero friction). Find: (a) What is the acceleration a of block A immediately after release? (b) What is the tension T in the cable at this instant?
(c) What is the velocity VA of block A after it moved a distance of 5.0 inches from its initial position? Reminder: Draw free body diagrams. Show all your work. '—
o a) EAL958 var/51:
c532: 2,?3 Fae/57‘ PROBLEM #1 (20 points)
Given: P = 200 1b, Q = 300 1b. Neglect the weight of the members. Find: The reaction force components in x and y direction at A and D and the force components in x and y direction acting on member AB at C. Reminder: Draw free body diagrams. Show all your work. E = +5907—ZOO'5 lbs.
5 z 590? +7003 IL; 2‘ = «5865+ 4605' “=8 PROBLEM #2 120 points: Given: The 750 mm wide gate, which may pivot about the horizontal shaft A, is held in the
closed position by the preloaded spring. The mass density of oil is p0“ = 900 kg/m3 . Find: The compressive force exerted by the preloaded spring on the gate for which the gate is
on the verge of opening when the depth of oil is d = 1.8 m. Reminder: Draw the pressure distribution on the gate. Draw a free body diagram. Show all
your work. PROBLEM #3 Given: A cablepulley system as shown. Mass B has
a velocity of 6.0 ft/s up, as shown. Find: What is the velocity of mass A?
Show all your work. PROBLEM #4 Given: An aircraft takes off at point 0. The
trajectory of the ﬂight path is given by
y = 0.01 x2, where both x and y are in
meters. The pilot’s body mass is m = 80 kg.
When x = 100 m, the speed of the aircraft
is 90 m/s and the speed is increasing at a
rate of 13 m/sz. Find: (a) The force vector F5, in terms of unit vectors
E. and En . which the cockpit seat exerts on
the pilot’s body. (b) When the aircraft is directly above point A,
what are R, and (I), using cylindrical
coordinates with origin at 13, as shown? g 5;: S’OS’M/s 2= 34.3452—
é = 0.403 rwet/5 e = 43.710 Pal/s"— PROBLEM #5 Each of the following ﬁve subproblems labeled (a) to (e) is worth 4 points and no partial
credit will be given. (a) Given: m. = 2.0 kg, m; = 5.0 kg; the mass of the rod connecting the two masses is
negligible. Find: Location of the x coordinate of the center of mass of the system. 7:6 30,184: M (b) Given: F = 4000 N Find: FOrces in truss members AC and BC. Indicate if the forces are in compression
or tension. RoooA “L6. (C) Given: F = 5000 N, M = 3000 Nm Find: Moment about point A due to the force F and the couple M. z/m,= [ooo Nm (d) Given: m = 100 kg. R = 0.5 m, [.15 = 0.1, cylinder is ﬁxed. Find: Minimum force F required for static equilibrium. .f’ [5 (e) Given: Two planes fly at the same altitude as shown. Find: The velocity of plane B relative to plane A, 33m , in units of km/hr. {fr3M; 1170; +3445 km/w ME 270 Final Examination Name
(Print) (Last) (First)  Instructor PROBLEM #4 125 points) Given: The mass of the piston B is mB = 2.0 kg. The slotted arm AB rotates, in the horizontal
plane, with 9: 0.5 rad/s = constant. The system has zero friction. .Find: At the instant when 9 = 60° , determine the force N; normal to the slotted arm that the arm
exerts on the piston, and the force N2 normal to the guide bar that the guide bar exerts on the piston. Use cylindrical coordinates with the origin at A! N, = wax/v
le 0.17M ...
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 Summer '08
 MURPHY
 Force, Mass

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