hrly_exam_i_vb.20070919.46f17812c4c7e8.37129247

# hrly_exam_i_vb.20070919.46f17812c4c7e8.37129247 - Name SS...

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Unformatted text preview: Name SS# Section TAM212 - Hour Exam 1 - Spring 2005 • Put your name on each sheet of work • Show all work on these exam sheets • Please write clearly and legibly Formula Sheet: Cylindrical coordinates: ˙ vp = r e r + r θ e θ + z k ˙ ˙ 2 ˙ ¨ ap = r − r θ er + r θ + 2rθ eθ + z k ¨ ˙˙ ¨ Intrinsic Coordinates: vp = set ˙ ap = set + ¨ s2 ˙ en ρ Coordinate Transformation: g replacements j eθ er = cos θ i + sin θ j eθ = − sin θ i + cos θ j er θ i = cos θ er − sin θ eθ i j = sin θ er + cos θ eθ Coefﬁcient of restitution: e= vBf − vAf vAi − vBi Rigid Body: velocity & acceleration ˙ vB = vA + θb k × rAB 1b ¨¨¨¨¨¨¨  ¨¨¨¨¨¨¨ ¨¨¨¨¨¨¨ ¨¨¨¨¨¨¨ ¨¨¨¨¨¨¨ y 2b A    ¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨ ¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨ ¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨ §© ¨§© §© ¨©¨©¨ §©¨§¨§¨§©  ¨©¨©¨§© §©§©¨§¨§¨ ¨§©¨§©¨§©  ¨©¨©¨ §©¨§¨§¨§© ¨§¨§¨§© ©¨©¨  ©§©¨©¨©¨ §¨§¨§¨§© ©¨©¨©¨ §¨§¨§¨ ¨¨¨§©§©  B c) y = −x/3 ˙ ˙ d) y = x/2 ˙ ˙ e) y = −x/2 ˙ ˙ a) y = −x ˙ ˙ b) y = x ˙ ˙ x  ¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨ ¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨ ¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨ ¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨ A3) Block A is being pulled up by moving block B to the right. If coordinates x and y are deﬁned as shown in ﬁgure which of the following relation is accurate. e) can not say since the radius of the orbit is not known b) no acceleration because of the constant speed c) radial acceleration pointed towards the center of Earth d) acceleration tangential to the path speed it has a) radial acceleration pointed away from the center of Earth A2) When a satellite revolves around the Earth in a circular orbit with constant ¦¦¦ ¦¦¦ ¥¡¥¡¥¡¥¡¥¡¥¡¥¡¦ ¡¦¡¦¡¦¦¡¡¦¡¦¡¥¡ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ££¤¤¡¡¡ ¥¡¥¡¥¡¥¡¥¡¥¡¥¡¦¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¡£¡£¡ ¡£¤¡£¤¡ ¤¤ ¡¤£¡¤£¡ ¦¦¡¡¦¡¦¡¦¦¡¡¦¡¥¡¦¦¡¡¦¡¦¡¦¦¡¡¦¡¦¡¦¦¡¡¦¡¦¡¦¦¡¡¦¡¦¡¦¦¡¡¦¡¦¡¦£¤¡¤¡¤¡ ¥¡¥¡¥¡¥¡¥¡¥¡¥¡¦¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡£¡£¡£¤ ¦¡¦¦¡¡¦¡¦¡¦¦¡¡¥¡¦¡¦¦¡¡¦¡¦¡¦¦¡¡¦¡¦¡¦¦¡¡¦¡¦¡¦¦¡¡¦¡¦¡¦¦¡¡¦¡¦££¤¡£¡£¡ ¥¡¥¡¥¡¥¡¥¡¥¡¥¡¦¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¡¤¡¤¡ ¡¡¦¡¡¡¡¦¡¥¡¦¡¦¡¦¦¡¡¦¡¦¡¦¦¡¡¦¡¦¡¦¦¡¡¦¡¦¡¦¦¡¡¦¡¦¡¦¦¡¡¥¦¥¤¡¡¡£¤£¤ ¢ ¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡¡£¡£¡ ¡¢ ¡¢ ¡¡¦¡¡¡¡¦¡¡¡¡¦¡¡¡¡¦¡¡¡¡¦¡¥¦£¤¡¡¡¤¤££¤ ¤¤¤ £¡£¡£¡ ¡£¤¤¡£¤¤¡ ¢¡ ¡ ¡ ¡¢¡¢¡ ¢¡ ¡ ¡ ¢ ¡¢¡¢¡¡ £¤¡¤¡¤¡£ ¢¡ ¡ ¡ ¢ ¡¢¡¢¡ ¢¡ ¤¡£¡£¡¤£¤£¤ ¢¡¢¡¢¡ ¢¡ ¡ ¢¡ ¢¡¡ ¡£¤¡£¤¡ ¢¡ ¡ ¡ ¡ ¡ ¡ ¡ £££¤¡£¡£¡ ¡¤¡¤¡£ ¢¡¡¡¡ ¢¡¢¡ ¢¢ ¡ ¡ ¡ ¢¡ ¤¤¡¤¡¤¡¤ £¡£¡£¡ ¡¤¡¤¡£ ¡£¡£¡¤ £¤¡¤¡¤¡£ ¡£¡£¡¤ £¤¡¤¡¤¡£ ¡£¡£¡¤ £¤¡£¤¡£¤¡¤£¤£ £¡£¡£¡£¤£ ¤£¤¡¤¡¤¡ £¤¡£¤¡£¤¡ ¤¡¤¡¤¡¤ £¡£¡£¡ ¡¡¡£¤££¤ g replacements Initial Compression 2m d) k N-m e) 4k N-m a) −3k/2 N-m b) 0 N-m c) −6k N-m Initially the spring is compressed by 2 m as shown in the ﬁgure. If the block moves to the right by 6 m, how much work is done by the spring? A1) A block of mass, m kg, is attached to a spring of spring modulus, k N/m. Circle your answer CLEARLY in the multiple choice questions PART A: Answer ALL of the following Name SS# Section Name SS# Section A4) Acceleration of a body in rectilinear motion is given in terms of its position as, a = x. If the initial velocity of the particle at x = 1 m is v = 1 m/s, ﬁnd the velocity at x = 3 m. a) 9 m/s b) 10 m/s c) 3 m/s d) 0 m/s e) 5 m/s A5) Balls A and B of equal mass approach each other with speeds 3 m/s and 1 m/s, respectively, as shown in ﬁgure. If collision is perfectly elastic, ﬁnd the velocities of A and B. j placements 3 m/s 1 m/s A B a) vA = −3i m/s b) vA = 1i m/s c) vA = −1i m/s vB = 1i m/s vB = 1i m/s vB = 1i m/s d) vA = 3i m/s e) vA = −1i m/s vB = −1i m/s vB = 3i m/s i 3b Name SS# Section B1) Block B1 in ﬁgure, which slides in a vertical slot, is pinned to bars B2 and B3 at A. The other ends of B2 and B3 are pinned to blocks that slide in horizontal slots. Block B4 translates to the left at constant speed 0.4 m/s. a) Find the velocity of point B at the given instant; b) Find the velocity of point A when C has moved to point D B1 PSfrag replacements A 3.5 m B2 B B3 2.5 m D 4b 3.3 m C B4 5b ¢¢ ¡ ¡ ¤ £¡ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¡ ¡ ¢ ¡£¤¡¡£¡£¡£¤¡¡£¡£¤¡¡£¡£¡£¤¡¡£¡£¤¡¡£¡£¤¡¡£¡£¤¡¡£¡£¤¡¡£¡¤¡ ¢¡¢¡¡ ¤¡¡¡¤¡¡¡¡¤¡¡¡¤¡¡¡¡¤¡¡¡¤¡¡¡¤¡¡¡¤¡¡¡¤¡¤¡£¤£¤ ¢¡¡ ¢¢¡ ¤¡¤£¡¡¤¡¤¡¤£¡¡¤¡¤£¡¡¤¡¤¡¤£¡¡¤¡¤£¡¡¤¡¤£¡¡¤¡¤£¡¡¤¡¤£¡¡£¡ ¡¢¡ £¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡ ¡ ¡ ¦ ¥¡¦ ¦ ¢¡¡¡ ¡ ¢¡ ¦¡¥¡¥¡ ¥¡¦¡¦¡ ¦¡¥¡¥¡¦ ¥¡¦¡¦¡¥ ¢¡¢¡¢ ¡¢¡ ¡ ¦¡¥¡¥¡¦  © §¨ ¥¡¦¡¦¡¥ ¦¡¥¡¥¡¦ ¥¡¦¡¦¡¥ ¢¡ ¡¢¢¡ ¦¡¥¡¥¡¦ ¥¡¦¡¦¡ ¡¥¡¥¡¦¥ ¦¡¡¡¥¦¥¦¥ ¦¡¦¡ ¥¡¥¡¥¡ ¢¡¢¡ ¡ ¡ ¡ ¡¢¡ ¡ ¡ ¢¢¡ ¢¡¡¡ ¡¢¡ ¢¢¡¢¡¢ ¡ ¡ ¢¡ ¡¡¡ b) How much mechanical energy is lost during collision? c) Assuming that the spring (k = 8 N/m) is initially at its natural length, what is its subsequent maximum compression? 20 kg as pictured and imbeds within the block. a) what is the speed of the bullet/block composite immediately after collision? B2) A bullet of mass 0.02 Kg, going at a speed of 200 m/s strikes a block of mass Name SS# Section ...
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## This note was uploaded on 04/17/2008 for the course TAM 212 taught by Professor Keane during the Fall '08 term at University of Illinois at Urbana–Champaign.

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