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CE 261 DYNAMICS

MIDTERM 2:

SHOW ALL WORK OPEN BOOK, CLOSED HOMEWORK OR SOLUTION MANUALS

ONE PAGE NOTES PERMITTED, NO CREDIT FOR ANSWER ONLY

1.	Two spheres of equal mass m = 3.73 kg are able to
slide along the horizontal rotating rod. They are
initially latched in position at a distance r = 0.5 m from
the rotating axis with the assembly rotating freely with
an angular velocity o = 100 rad/sec. After the spheres
are released they assume positions at the ends of the
road at a radial distance of 3 r. Neglect the mass of the
rod and shaft.

A.	Determine the new angular velocity, .

B.	Find the fraction n of the initial kinetic energy of the system which is lost as a result of the outward motion, collision and latching of the spheres in the new position.

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2.	Given rod as show to the right which moves with an angular velocity, = 20 rad/sec, and angular acceleration (CCW) , = -1 rad/sec2 (CW), and a slider A which moves along the rod outwards with a velocity of 2 m/sec which decelerates at -1 m/sec2.

A.	Find the absolute velocity of the slider A, VA .

B.	Find the absolute acceleration of the slider A, aA.

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3.	Ball B of mass 1 kg is hanging from an inextensible cord. An identical ball A is released from rest when it is just touching the cord and drops through the vertical distance hA = 150 mm before striking ball B. The coefficient of restitution e = 0.8.

A.	Calculate the velocity of ball A just before impact.

B.	Assuming the velocity of ball A is 2 m/s just before impact, calculate the velocity of ball B just after impact. (Hint: conservation of impact momentum is obeyed in x direction, not in normal impact direction due to cable tension, also ball B must move in the x direction initially due to cord)

C.	Calculate the resulting maximum vertical displacement, hB, of ball B if the velocity of ball B after impact is 1 m/sec.

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4.	The uniform pole AB weighs 150 lb and is suspended in the horizontal position by the three wires shown. If the wire CB breaks, the pole AB moves down and to the right.

A.	Draw a free body diagram of AB, indicate with a dotted arrow the direction of acceleration of the bar's mass center aG.

B.	Find the initial angular velocity and angular acceleration of the pole AB about its mass center G.

C.	Find the tension in wire BD.

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5.	A spacecraft orbits the moon in a circular path of 80 km altitude.

A.	Calculate it velocity. Ignore presence of earth.

B.	If its rocket engine is activated to produce a sudden bust of speed, determine the increase V necessary to allow the spacecraft to escape from the moon's gravity field. Ignore presence of earth.