Accurate Vector Diagram - General Physics - Past Paper, Exams of Physics

Download Accurate Vector Diagram - General Physics - Past Paper and more Exams Physics in PDF only on Docsity! AJM:1/6/04 Score /100 Physics 131 Midterm Winter 2002 Name PLEASE READ THIS FIRST: Work the problems on separate sheets of paper and staple this sheet to the front. Read each problem carefully and be sure to pay attention to any hints that are provided. The credit you receive on each problem will depend at least as much on how you get your answer as on what answer you get. There is no need to be as “wordy” as I ask you to be on homework, but you must show your work or give at least a brief explanation for every answer. I give no credit for unsupported answers. I give partial credit for partially correct solutions, but only when I can figure out what you are doing, so be as clear as possible. Make certain that all numerical answers are given with a reasonable number of significant digits (when in doubt, three is usually a good compromise) and that you have included appropriate and simplified units. Check your answers for physical reasonableness whenever possible; I do deduct a small number of points for ridiculous answers that go uncommented upon. 1. [10 pts] A speeding driver spots a policeman on the road ahead and slows her speed from 40 m/s (~90 mph) to 25 m/s (~55 mph) in 6.0 s. Assuming that the acceleration is constant, how far does she travel as she slows down? 2. [10 pts] Suppose you have a motor boat with a top speed of 20 km/hr on a river that flows at 8.0 km/hr. How long a time will it take you to travel 5.0 km downstream and back? [Hint: Find the speed of the boat relative to the shore.] 3. Exactly three constant forces act on an object that is initially at rest. As a result, the object attains a speed of 15.0 m/s after 5.0 seconds. The three forces are r F 1 = 40.0 N, south; r F 2 = 20.0 N, east; and r F 3 = 50.0 N, 20° north of west . a) [4 pts] Draw a reasonably accurate vector diagram showing how you would graphically add the three forces to obtain the resultant force r F net . b) [12 pts] Find the net force and express it in “magnitude, direction” format. c) [4 pts] What is the mass of the object? 4. You throw a rock at an angle 60° above the horizontal off the edge of a cliff and into a lake below. It hits the water 6.0 seconds later at a horizontal distance 72 m from the cliff. a) [8 pts] How fast was the rock moving when it left your hand? [Hints: Use the “method” and find the horizontal component of the initial velocity.] b) [12 pts] How high is the cliff? 5. [20 pts] A crate slides down a 20° incline while slowing down at a rate of 1.0 m/s2. What is the kinetic coefficient of friction between the block and the surface of the incline? [Hint: Use the “method.”] EXTRA CREDIT [5 pts] What would the acceleration of this crate be if it were sliding up this incline? 6. [20 pts] A 50 gram ball hangs from a 2.0 m long string attached to the ceiling and moves in a horizontal circle such that the string always forms a 40° angle with the vertical as shown at right. How long a time will it take the ball to complete one revolution around its circular path? [Big hints and required elements of a full credit solution! 1) Find the radius of the circular path. 2) Draw an appropriate free body diagram for the ball that includes its acceleration vector. 3) Indicate your choice of coordinate system. 4) Apply Newton’s second law to the ball. 5) Obtain the component equations that follow from your free body diagram and your coordinate system.] EXTRA CREDIT [5 pts] Even if you were not able to solve this problem you can still determine how the answer depends on the m, L, and g using nothing but dimensional analysis. Explain, clearly and specifically, how. θ = 40° L = 2.0 m m = 50 g