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Unformatted text preview: Problem #1 (20 points, 4 points each part) A m = 4lb collar can slide without friction along a horizontal rod and is released from
rest at A. The undeformed lengths of springs AB and AC are [A30 = 10 in. and [Ago = 9 in.,
respectively. The constant of each spring is k = 2800 lb/in. The mass is released at time I]. At a later instant of time t2 the collar has moved A = 1 in. to the right. a) What is the initial kinetic energy of the system T1? b) What is the initial length of the spring 1.? c) What is the initial potential energy of the system V1? (1) What is the potential energy of the system V2 at time t;?
e) What is the velocity v; of the mass at time t2, (in ft/s) Problem #2 (36 points, 4 points each part) A sphere rebounds as shown after striking a ﬁxed inclined plane with a vertical velocity VA] of magnitude V,“ = 5 m/s. The angle a: 30° and the coefﬁcient of restitution
COR = 0.8. Conditions just before the impact are de noted as 1, just after impact 1’, and when the ball is at maximum height is noted as 2. Deﬁne time tl E tl' = 0. a) Find the unit vector in the tangential direction (to the impact) et.
b) Find the unit vector in the normal direction (to the impact) en.
0) What is the velocity vector before the impact VA]? d) What is the tangential velocity after the impact (ﬁn) ‘7 t e) What is the normal velocity after the impact (v; l) ? H t) What is the velocity vector after the impact v'A , ? g) What is (1),”) in terms ofg, t2 , and (v91)? l h) Find time t2.
i) Find h. Problem #3 (44 points, 4 points each part) In a game of billiards, ball A is given an initial velocity VA. = 4 i (m/s) as shown. It hits
ball B at time t1 and then hits ball C. Balls B and C are both initially at rest. Ball B is
observed to hit the table obliquely at point B' at time t2, v32 = szx i + vazy j (components
unknown). A short time later, balls A and C are observed to hit the sides of the table at right angles,
at points A' and C', respectively. The distances are a = 1.65 m, c = 1.05 m, d= 1.5 m,
VA; = 1.92 m/s, and Va is unknown. The origin of the system is in the lower left hand comer. The mass of each ball is 0.17 kg. Assume the position of A and B is the same at initial
time t., and likewise the position of A and C is the same at the time of their impact (the
balls are small relative to the size of the table). a) Find the initial momentum of the system L1.
b) Find the momentum of the system L2 in terms of the mass and velocities at time 2 (known and unknown).
c) Find the initial position vectors of A and C: rm and re]. d) Find the initial position vector of the mass center F].
e) Find the initial position vectors of A and C relative to the mass center: 1'}; and rc’I . t) Find the initial angular momentum about the origin of the system H01. g) Find the angular momentum about the origin of the system H02 in terms of the
mass, positions and velocities at time 2 (known and unknown). h) Find the initial angular momentum about the mass center of the system HGI. i) Find the initial kinetic energy Tl. j) Find the velocities szx, szX and vcz (just explain in terms of equations and
unknowns — do not solve). k) What is your name? Name: RIN; Problem #1 (20 points, 4 points each part) T i?" W k = 2800 lb/m. 7”"?
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This note was uploaded on 04/06/2009 for the course ENGR 2090 taught by Professor Johntichy during the Spring '09 term at Rensselaer Polytechnic Institute.
 Spring '09
 JohnTichy
 Dynamics

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