advertisement

EXAM I, PHYSICS 1403 September 30, 2004 Dr. Charles W. Myles INSTRUCTIONS: Please read ALL of these before doing anything else!!! 1. PLEASE put your name on every sheet of paper you use and write on one side of the paper only!! PLEASE DO NOT write on the exam sheets, there will not be room! 2. PLEASE show all work, writing the essential steps in the problem solution. Write appropriate formulas first, then put in numbers. Partial credit will be LIBERAL, provided that essential work is shown. Organized, logical, easy to follow work will receive more credit than disorganized work. 3. The setup (PHYSICS) of a problem will count more heavily than the math of working it out. 4. PLEASE write neatly. Before handing in your solutions, PLEASE(!!!): a) number the pages and put the pages in numerical order, b) put the problem solutions in numerical order, and c) clearly mark your final answers. If I can’t read or find your answer, you can't expect me to give it the credit it deserves. NOTE: I HAVE 130 EXAMS TO GRADE!!! PLEASE HELP ME GRADE THEM EFFICIENTLY BY FOLLOWING THE ABOVE SIMPLE INSTRUCTIONS!!! FAILURE TO FOLLOW THEM MAY RESULT IN A LOWER GRADE!! THANK YOU!! A 8.5’’ x 11’’ sheet with anything on it & a calculator are allowed. Problem 1 (Conceptual Questions) IS REQUIRED! Answer any two (2) of the remaining problems for a total of three (3) problems required. Problem 1 is worth 34 points. Problems 2, 3, and 4 are equally weighted & worth 33 points each. 1. THIS PROBLEM IS REQUIRED!!! CONCEPTUAL QUESTIONS: Answer these briefly, in a few complete and grammatically correct English sentences. More credit will be given for WORDS than for equations! a. State Newton’s 1st Law and Newton’s 3rd Law. b. See figure. Suppose that you are riding in a convertible with the top down. The car is moving to the right (x-direction) at constant velocity v0x . You throw a ball straight up (from your viewpoint) with an initial velocity v0y while the car continues to travel forward at v0x. Neglect air resistance. Will the ball land behind the car, in front of the car, or in the car? WHY? Explain (briefly!) your answer. Use what you know about projectiles!. Make a sketch of the situation to illustrate your explanation. Answer the following for a 5 POINT BONUS! During our class discussion about projectiles, I did an in-class demonstration illustrating the answer to this question. Briefly describe this demonstration. (If you were in class the day I did this demonstration, you probably will be able to answer this. However, if you “cut” class that day, as many of you often do, you probably won’t be able to answer it!) v c. See figure. A box is sliding at constant velocity (v = constant!) across a flat, horizontal, frictionless surface. Sketch the free body diagram for this box. Is there a force in the direction of the box’s motion? Explain your answer using Newton’s Laws! NOTE: Answer any two (2) of problems 2, 3, & 4!!! 2. See figure. A person stands a horizontal distance d from the base of a building. He throws a ball from the ground towards the building. Its initial velocity is v0 = 25 m/s at an initial angle θ0 = 30º with respect to the horizontal. It hits the building at a height h above the ground. At the point where it hits, its vertical component of velocity vy = 0 (that is, at that point, its velocity is entirely in the horizontal direction.) a. Compute the x and y components, vx0 and vy0, of the initial velocity. b. Compute the time it takes the ball to hit the building. c. Compute the height h where the ball hits the building. d. Compute the distance d from the base of the building where the thrower is standing. e. Compute x and y components, vx and vy, of the ball’s velocity a time t = 0.75 s after it is thrown. Compute the magnitude and direction of the velocity vector v at that time. f. Compute the ball’s height at a time t = 0.75 s after it is thrown. d 3. See figure. A mass m = 15 kg is connected to a massless cord and placed on a horizontal, surface. It is then pulled to the right by a force FP = 45 N that makes an angle = 25° with the horizontal. There is no vertical motion. The coefficient of kinetic friction between the mass and the table is μk = 0.2. a. Draw the free body diagram for the mass, properly labeling all forces. b. Compute the horizontal (x) and vertical (y) components of the applied force FP. c. Write the equations which result from applying Newton’s 2nd Law to the mass in both the horizontal (x) and the vertical (y) directions. You will receive more credit by writing these with symbols, without numbers substituted in, than you will by writing them with numbers substituted in! d. Compute the normal force between mass and the horizontal surface. Is this force equal (and oppositely directed) to the weight mg? If so, why? If not why not? Justify your answer using the appropriate Newton’s 2nd Law equation from part c. e. Compute the frictional force, Ffr between the box and the surface. f. Using the appropriate Newton’s 2nd Law equation from part c., compute the acceleration a of the box. If it starts from rest, how far has it moved after t = 3 s? m I 4. See figure. Two masses (mI = 15 kg and mII = 25 kg) are connected by a massless cord over a massless, frictionless pulley as shown in the figure. The masses are then released, so that mI moves to the right with acceleration a and mII moves downward with the same acceleration. Assume that friction can be neglected. a. Draw the free body diagrams for the two masses, properly labeling all forces (call the tension in the cord FT). b. The two unknowns are the acceleration, a, of the masses and the tension, FT, in the cord. By applying Newton’s 2nd Law to the two masses, find the two equations needed to solve for a and FT. c. Using the equations from part b, calculate a and FT (in any order). d. Assuming that it starts from rest, compute the speed of the hanging mass mII and the distance it has fallen after a time t = 2 s. mII