EXAM II, PHYSICS 1403 July 21, 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! Yes, this wastes paper, but it makes my grading easier! 2. PLEASE show all work, writing the essential steps in the solutions. 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 55 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!! An 8.5’’ x 11’’ piece of paper with anything written on it and a calculator are allowed. NOTE: Problem 1 consists of Conceptual Questions and IS REQUIRED! You may work any three (3) of the remaining four problems for four (4) problems total for this exam. Each problem is equally weighted and worth 25 points, for a total of 100 points on this exam. 1. THIS PROBLEM IS MANDATORY!!! CONCEPTUAL QUESTIONS: Answer these briefly, in a few complete and grammatically correct English sentences. You may supplement these sentences with equations, but keep these to a minimum!! (Newton’s Laws are about forces! For full credit in parts a. & b., you must mention FORCES!) a. State Newton’s 1st Law. b. State Newton’s 3rd Law. c. See figure. A hockey puck slides to the right at constant velocity across a flat, horizontal, frictionless ice surface. Which of the sketches in the figure is the correct free body diagram for this puck? WHY? Explain your answer using Newton’s Laws! (Hint: Is there a force in the direction of the puck’s motion?) d. See figure. A Ferris wheel rider moves in a vertical circle of radius r at constant speed v. He thus experiences a centripetal acceleration a. The free body diagrams for the rider at the top and at the bottom are shown in the figure. Is the normal force FN that the seat exerts on the rider at the top of the circle less than, more than, or the same as the normal force at the bottom of the ride? (Is FN equal to the weight?) Explain your answer using Newton’s 2nd Law with centripetal acceleration. NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!! 2. See figure. Two masses (m1 = 15 kg and m2 = 25 kg) are m1, a connected by a massless cord over a massless, frictionless pulley as shown. m1 sits on a flat, horizontal frictionless table. The system is released and m1 accelerates to the right while m2 accelerates downward. a. Draw the free body diagrams for the two masses, properly labeling all forces. For m1, be sure to include both horizontal and vertical forces. b. Compute (find a numerical value for) the normal force FN between m1 and the table. c. The two unknowns in this problem are the acceleration, a, of the masses (assumed to be the same magnitude for both) and the tension, FT, in the cord. By applying Newton’s 2nd Law to m1 and m2, find the two equations needed to solve for a and FT. Writing them in symbols, without substituting in numbers, will receive more credit than writing them with numbers substituted in! d. Using the equations from part b, compute (find numerical values for) the acceleration a and the tension FT (in any order). 3. See figure. A box, mass m = 25 kg, is placed on a flat, horizontal surface. There is friction. The coefficient of kinetic friction between the box and the surface is μk = 0.2. The box is pulled a by a force FP = 70 N using a cord that makes a 37º angle with the horizontal. a. Draw the free body diagram for the box, properly labeling all forces. b. Compute the horizontal and vertical components of the force FP. c. Compute the weight of the box and the normal force FN between it and the surface. Is this normal force equal (& oppositely directed) to the weight? If so, why? If not why not? Justify your answer using Newton’s 2nd Law in the vertical direction. d. Compute the frictional force Ffr that the box experiences as it moves to the right. e. Use Newton’s 2nd Law to find the acceleration experienced by the box. What forces cause this acceleration? m2 a NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!! 4. See figure. A planet, mass m = 3.0 x 1024 kg, is in a circular orbit at a constant speed v around a star, which is assumed to be a uniform sphere of constant density. The radius of the orbit (measured from the star’s center) is r = 3.0 x 1011 m. The mass of the star is M = 2.0 x 1030 kg. The gravitational constant is G = 6.67 x 10-11 N m2/kg2. a. The planet’s orbit is circular, so it experiences a centripetal acceleration. Using words (not equations, for which I will give zero credit!) tell me what the cause of this acceleration is. (Hint: See part b!) Circular orbit! b. Compute the gravitational force of attraction FG between the planet and the star. What is the “centripetal force” on the planet? (Hint: Answers to a & b should be consistent! You do not need to know the planet’s speed to answer this!) c. Compute the centripetal acceleration experienced by the planet. What is the direction of this acceleration? (You do not need to know the planet’s speed to answer this!). d. Compute the speed v of the planet in orbit. (Hint: Einstein taught us that the largest speed possible for anything is the speed of light c = 3 × 108 m/s. If you get a speed larger than this, you’ve done something wrong!) e. Compute the period T of the planet’s orbit. 5. See figure. A ball, mass m = 2.5 kg is twirled at constant speed v = 4 m/s at the end of a massless string in a vertical circle of constant radius r. The period for this uniform circular motion is T = 1.6 s. Free body diagrams for the ball at the top and at the bottom of the circle are shown. a. Compute the radius r of the circle in which the ball is moving. b. Compute the ball’s centripetal acceleration. c. Compute the “centripetal force” on the ball. d. When the ball is at the top (point A in the figure) compute the tension FTA in the string. e. When the ball is at the bottom (point B in the figure) compute the tension FTB in the string.