Physics I [Phys 161]                             Spring 2005 Assignment #4 Problems For Exam 2, you will be expected to do problems of difficulty similar to those below without reference to the text or to any notes.  Make sure that you can do this before you move on to the next assignment! Graded Homework Problems Do Assignments 4A and 4B at www.masteringphysics.com .   Mandatory Homework Problems (1) Based on your observation and experience, draw a motion diagram showing the position, velocity, and acceleration vectors for a pendulum that swings in an arc carrying it from an initial position 45° to the right of the central vertical line to a final position of 45° to the left of the central vertical line.  The arc is a quadrant of a circle, and you should use the center of the circle as the origin for the position vectors. (2) A rock is thrown upward from the level ground in such a way that the maximum height of its flight is equal to its horizontal range d.  (a) At what angle q is the rock thrown?  (b) Would your answer to part (a) be different on a different planet?   (3) Young David who slew Goliath experimented with slings before tackling the giant.  He found that he could revolve a sling of length 0.600 meters at the rate of 8.00 rev/s.  If he increased the length to 0.900 meters, he could revolve the sling only 6.00 times per second.  (a) Which rate of rotation gives the greater speed for the stone at the end of the sling?  (b) What is the centripetal acceleration of the stone at 8.00 rev/s?  (c) What is the centripetal acceleration at 6.00 rev/s? (4) An aluminum ball is attached to the end of a string and whirled in a circular path in the horizontal plane (xy-plane).  The length of the string from the center of the circle to the center of the aluminum ball is 1.5 meters, and the ball travels at a constant speed of 12 m/s in the counterclockwise direction.  The origin of the xy-plane is taken to be the center of the circle. At the instant that the ball is at the position x = 1.5 meters, y = 0 meters….     (a) Draw the r-hat and theta-hat vectors at this position. (b) Is the tangential velocity of the ball at this point in its motion zero?  If not, what is it? (c) Is the tangential acceleration of the ball at this point in its motion zero?  If not, what is it? (d) Is the radial velocity of the ball at this point in its motion zero?  If not, what is it? (e) Is the radial acceleration of the ball at this point in its motion zero?  If not, what is it? (f) Is the centripetal acceleration of the ball at this point in its motion zero?  If not, what is it? (g) Is the ball being subjected to a centripetal force at this point in its motion?  Explain. (5) A coin placed 30.0 cm from the center of a rotating, horizontal turntable slips when its speed is 50.0 cm/s.  (a) What force causes the centripetal acceleration when the coin is stationary relative to the turntable?  (b) What is the coefficient of static friction between the coin and the turntable? (6) A sign of mass 30 kg. hangs at rest from two cables, as shown below. SHAPE  \* MERGEFORMAT Determine the tensions, TL and TR, in the left and right cables, respectively.