Period of Motion - General Physics - Past Paper, Exams of Physics

Download Period of Motion - General Physics - Past Paper and more Exams Physics in PDF only on Docsity! AJM:12/14/01 Score /100 Physics 131 Final Exam Fall 1997 Name Please work the problems on separate sheets of paper and staple this sheet to the front. Read each problem carefully. Show your work and/or give explanations for all answers. Make sure that your answers are given with a reasonable number of sig figs and that you have included appropriate units. Check your answers for physical reasonableness whenever possible. I do give partial credit, but only if I can follow your work, so try to be clear about what you are doing. 1. [20 pts] A dragster starts from rest and finishes a race of one-quarter mile in 5.60 s. Assuming it moves with constant acceleration ... a) what is its final speed? Express your answer in ft/s AND in mi/hr. (1 mi = 5280 ft) b) what is its acceleration? Express in ft/s2 AND in “g’s ” where 1 “g” = 9.80 m/s2 = 32.2 ft/s2. c) [5 pts “extra credit”] What is the minimum coef. of friction between the tires and the road? 2. A body is attached to the ceiling by a string of length L and moves in a horizontal circle with the string at a constant angle θ to the vertical. a) [15 pts] Find the period of motion (the time it takes to complete one trip around the circle) in terms of L, θ, and g. [Hints: Apply Newton’s second law to the body and find the radius of the circle in terms of L and θ.] b) [5 pts] Sketch a plot of the period of motion as a function of θ. Comment on what happens to the period as θ increases and on the limiting values of the period as θ approaches 0° and as θ approaches 90°. 3. A small body is released from rest at the highest point of the frictionless hemispherical bowl shown at right. It subsequently collides with and sticks to an identical body resting at the lowest point. a) [15 pts] Find the maximum angle θ reached by the two bodies after the collision. b) [2 pts] Why is the gravitational potential energy of the two bodies at the angle θ NOT equal to the initial gravitational potential energy of the first body? c) [3 pts] Describe what would have happened if the collision (and any subsequent collisions) had been elastic? 4. An 80 kg man stands 1/4 of the way from the right end of a uniform beam that is supported in its horizontal orientation only by two wires as shown at right. a) [20 pts] What is the mass of the beam? b) [5 pts “extra credit”] Find the minimum radius of the wire with the greatest tension if it is made of steel and we want not to exceed its elastic limit of 3 x 108 N/m2. 5. Three children, each with a mass of 35 kg, are playing on a playground merry-go-round of radius 2.0 m and moment of inertia 600 kg m2. All three children are at the outer edge of the merry-go-round having jumped on when its tangential velocity was equal to their maximum running speed of 5.0 m/s. a) [5 pts] What is the angular velocity of the merry-go-round? Now two of the children move to the center of the merry-go-round. b) [10 pts] What is the new angular velocity of the merry-go-round? c) [5 pts] What is the net force acting on the child who is left at the edge? d) [5 pts “extra credit”] What is the ratio of final to initial kinetic energy of the merry-go-round and children? Comment on the meaning of and explain your answer. θ L θ 140° 120°