Name ___________________________ Section _____________________ ES204 Examination II January 22, 2004 Problem Score 1 /30 2 /30 3 /40 Total /100 Show all work for credit AND Turn in your signed help sheet AND Stay in your seat until the end of className 30 pts ES204 Examination II Problem 1 Jan. 22, 2004 1.1 At the instant shown, where is the instantaneous center of zero velocity for rod AB assuming the disk rolls without slipping on the ground? The regions are shown be dotted lines. a) region 1 b) region 2 c) region 3 d) region 4 e) region 5 f) region 6 1.2 The tire rolls without slipping down the incline. The energy of the tire is equal to its kinetic energy plus its gravitational potential energy. Which of the following statements is true? a) The energy of the tire at position 1 is greater than the energy of the tire at position 2 b) The energy of the tire at postion 1 is less than the energy of the tire at position 2 c) The energy of the tire at postion 1 is equal to the energy of the tire at position 2 d) We can’t determine in which position the tire will have a larger energy until we have defined a datum for the problem. Explain your answer: 1.3 At the instant shown, the cables rotate with the given ω and α and are both cables at angles of 15 degrees from vertical. What is the angular velocity of the plate at this instant? a) 0 rad/s b) 1 rad/s c) 2 rad/s d) 3 rad/s e) not enough information given (you need the length of the cables). 1 2 3 4 5 6 A B C 6 Position 1 Position 2 ω= 1 rad/s α=2 rad/s2 20in 20in A BC cm1.4 If ˆkω=ωr rad/s and jˆ3iˆ4r +=rm determine rω×rr 1.5 For the object shown below what is the magnitude of the angular momentum about point A? a) 0 b) mvGa c) mvGb d) 22Gmv a b+ 1.6) The table shown below starts from rest and speeds up so that the block experience a constant tangential acceleration, at. Assume the block does not slip on the table. What is the direction of the friction force when the speed of the block is, v? Circle the direction the best shows the direction of the friction force. Top View a a mvG b b AName 30 pts ES204 Examination II Problem 2 Jan. 22, 2004 The gear has a mass of 2 kg and a radius of gyration of 0.19 m. The connecting link (slender rod) and the slider block at B have a mass of 4 kg and 1 kg, respectively. If the gear is released from rest in the position where θ = 30º, determine the equations necessary to determine the angular velocity of the gear when θ = 0º as shown in position 2. Only a portion of the two tracks are shown. Do not solve the equations. Your solution should consist of a clear list of equations and unknowns. A B 0.6 m 0.2 m 45° θ =30° A B Gear Position 1 Position 2 Unknowns Equation NumberName 40 pts ES204 Examination II Problem 3 Jan. 22, 2004 The uniform pole has a mass of 15 kg and falls from rest when θ = 90º until it strikes the edge at A, θ = 60º. If the pole begins to pivot about his point after contact, determine the equations necessary to determine the reactions at point A immediately after the impact. Assume that the pole does not slip at B as if falls. Do not solve the equations. Your solution should consist of a clear list of equations and unknowns. 3 m A B C θ 0.5 m Unknowns Equation