hrly_exam_ii_vc.20070919.46f178c96b9d91.67723657

hrly_exam_ii_vc.20070919.46f178c96b9d91.67723657 - Name...

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Unformatted text preview: Name Section TAM212 - Hour Exam II - Spring 2005c • 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 1 Name Section Rigid body: velocity and acceleration ˙ vB = vA + θb k × rAB ¨ ˙ aB = aA + θb k × rAB − (θb )2 rAB Two different frames: velocity and acceleration ˙ vP |F = vP |B + vO |F + θB k × rO P ¨ ˙ ˙ aP |F = aP |B + aO |F + θB k × rO P − (θB )2 rO P + 2θB k × vP |B Rolling of a wheel of radius (r ) on a curved plane of radius (R) ˙ vC = −r θ et ˙ (r θ)2 ¨ en aC = −r θ et + ρ where ρ = R ± r Parallel axis theorem P C Izz = Izz + md2 P C Ixz = Ixz − mxz ¯¯ P C Iyz = Iyz − myz ¯¯ 2 Name Section PART A: Answer ALL of the following Circle your answer CLEARLY in the multiple choice questions A wheel rolls on the floor and drags a rod which is pinned to the wheel A1) at A. The center of the wheel, C, moves to the right with a constant speed of 20 m/s. Find the velocity of B at the instant shown. A 4m placements C a) 20 i m/s b) 5 j m/s c) 15 i m/s 20 m/s 1m d) 10 j m/s e) 40 i m/s B ¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ ¢ ¢ A2) In the above problem at the instance shown, which of the following is true about the rod AB? a) nonzero angular velocity and zero angular acceleration b) nonzero angular velocity and nonzero angular acceleration c) zero angular velocity and zero angular acceleration d) zero angular velocity and nonzero angular acceleration e) none of the above A full sphere of radius R with uniform density has a moment of inertia A3) 1 kg -m . A smaller sphere of radius R/2 is cut out from center of the full sphere (see figure). What is the moment of inertia of the hollow sphere? 2 £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ R/2 £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ £¤£¤ placements a) 1/32 kg -m2 b) 1 kg -m2 R c) 2/5 kg -m2 d) 1/2 kg -m2 e) 31/32 kg -m2 3 Name A4) Section For the given figure, which of the following statements is true z C a) Ixy = 0, C b) Ixy = 0, C Ixz = 0, C Ixz = 0, C Izz = 0 C Izz = 0 C c) Ixy = 0, C d) Ixy = 0, C e) Ixy = 0, C C Iyz = 0, C Iyz = 0, C Iyz = 0, C Iyz = 0, C Iyz = 0, C Ixz = 0, C Ixz = 0, C Ixz = 0, C Izz = 0 C Izz = 0 C Izz = 0 y x A5) The cylindrical tank is rolling backward without slipping on the flatbed of a truck. The center of the tank has a velocity of 10 ft/s to the left (relative to the ground), and the truck has a forward speed of 30 ft/s. Determine the angular velocity of the tank. 10 ft/s R = 8 ft 30 ft/s placements ¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ ¢ ¢ 4 a) 5 rad/s b) 10 rad/s c) 20 rad/s d) -5 rad/s e) -20 rad/s Name Section PART B: Answer ALL of the following B1) A cart (plus 4 wheels) of mass 500 kg is pushed up a hill with a force of T Newtons at a height 2.7 m as shown in the figure. The wheels have no friction. Determine the largest force for which the cart will not tip. Also determine the acceleration of the cart. g y x C T 3 PSfrag replacements 4 2m 2.7 m 1m 1m 5 Name B2) Section The rod AB, shown in figure, rotates clockwise such that it has an angular velocity ωAB = −2 rad/s and angular acceleration αAB = −3 rad/s2 when θ = 45◦ . Determine the angular motion of rod DE at this instant. The collar at C is pin connected to AB and slides over rod DE. 0.4 m B C E D ωDE , αDE y PSfrag replacements x 0.4 m ωAB = −2 rad/s, αAB = −3 rad/s2 θ = 45◦ A 6 ...
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