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Exam #1 PHYS 201-1M 13 September 2006 Name_________________________ Answer each of the following questions. Circle your final answer. Full credit will be given only for the correct answer. For errors in the calculations but where the method is correct, only one point will be deducted. If the chosen method is incorrect, no credit will be given for that section of the problem. However, if subsequent questions depend on the missed answer, no points will be deducted if the method and calculations for those sections are correct, even though the final answer may be wrong. 1) (15 pts) In this figure, a crate of mass m=200 kg is pushed at a constant speed up a frictionless ramp (θ=35○) by a horizontal force. What are the magnitudes of r a. (7 pts) F ? b. (8 pts) The force on the crate from the ramp? 2) (15 pts) A woman rides a carnival Ferris wheel with radius of 20 m, completing 4 turns about its horizontal axis every minute. What are a. (3 pts) The period of the motion b. (3 pts) Magnitude of her centripetal acceleration at the highest point c. (3 pts) Direction of her centripetal acceleration at the highest point d. (3 pts) Magnitude of her centripetal acceleration at the lowest point e. (3 pts) Direction of her centripetal acceleration at the lowest point 3) (20 pts) In this figure, a ball is thrown up onto a roof, landing 5.00 s later at a height of h=25.0 m above the release level. The balls path just before landing is angled at θ=55○ with the roof. a. (6pts) Find the horizontal distance d the ball travels. b. (7 pts) What is the magnitude of the ball’s initial velocity? c. (7 pts) What is the angle (relative to the horizontal) of the ball’s initial velocity? r 4) (20 pts) The position r of a particle moving in an xy plane is given by r r r = (3.00t 3 − 6.0t )iˆ + (5.00 − 8.00t 5 ) ˆj , with r in meters and t in seconds. In unitvector notation, calculate, when t=3.00 seconds r a. (5 pts) r r b. (5 pts) v r c. (5 pts) a d. (5 pts) What is the angle between the positive direction of the x-axis and a line tangent to the particle’s path at t=3.00 seconds? 5) (10 pts) Oasis B is 30 km due east of Oasis A. Starting from Oasis A, a camel walks 23 km in a direction 15○ south of east and then walks 7.0 km due north. How far is the camel then from Oasis B? 6) (20 pts) The position of a particle moving along an x-axis is given by x = 10t 2 − 3t 3 , where x is in meters and t is in seconds. Determine a. (2 pts) The position when t=4.0 s b. (3 pts) The velocity when t=4.0 s c. (3 pts) The acceleration when t=4.0 s d. (3 pts) What is the maximum positive coordinate reached by the particle? e. (3 pts) At what time did it reach this maximum positive coordinate? f. (3 pts) What is the maximum positive velocity reached by the particle? g. (3 pts) At what time did it reach this maximum positive velocity?