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EM311M - Dynamics Exam 2 Monday, Oct 25, 2004 2 0 9o I o L - n L - 1. Let F denote the gravitational force exerted by Earth (with mass M) on a particle with mass m. located at position r = (x,y, z) with the origin of the system of coordinates at the center of the Earth. 1. Use the "sliding vector formula" to represent the Cartesian components of the force in terms of coordinates x, y, z. 2. Prove that the corresponding potenial is given by, (5 points) 2. Use the definition of work to compute the work done by a constant force F = (2.3) r; .. ., along the circle shown below. from point A to point B. (5 points) [kN] 3. The mass of A is 30 kg and the mass of B is 5 kg. A slides on the smooth surface with the angle B = 30" being constant. \+'hat is force F ? (5 points) ! , ' 4. Derive the principle of angular momentum for a system of particles with respect fixed point 0. (5 points) 5. Determine the IC of zero velocity for the bar connecting the two wheels shown below. ( 5 points) 6. The 1-kg collar A is attached to the linear spring (k = 500 N/m) by a string. The collar starts £rom rest in the position shown, and the initial tension in the string is 100 N. What distance does the collar slide up the smooth bar ? (25 points) 7. Two small balls, each of mass m = 0.12 kg, hang from strings of length L = lm. The left ball is released from rest with 8 = 30'. As a result of the initial collision. the right ball swings through a maximum angle of 25". Determine the coefficient of restitution. (25 points) 2-. 8. The crank AB has a constant clockwise angular velocity of m velocity and acceleration of the piston P? (25 points) ' Vq dp 1,89 r 4 I. y ? = Z Vp v,, - u b ~ - 7 e If:., 5tj - /v,*= ss.zr k: . -. s-c \ -J 7 k C. U,=A - 2 4 n - 2 C ~ ~ ? / CG~13,,, d: 0 0 (-1 - " ? b What are the 0 : -f-11,~= 9 - QO." (C. 6 ~ C S J ?,9 ' 5.-r ~ ~ ~