. Physics 0174(CHS) Exam #1 Academic Year 2015-2016 NAME This exam consists of 6 pages in addition to this page; please check to see that you have all of them. Be sure to show clearly how you arrive at your answers; even if an answer seems obvious, be sure to give some indication of how you got it (unless you are specifically told that no explanation is necessary). If a vector quantity is asked for, remember that simply giving its magnitude is not a sufficient answer (unless the magnitude is zero). Be sure to include units with your answers where appropriate. Failure to follow these instructions will result in lost points. Note that vectors are represented on this exam by boldface type, and the unit vectors are written as i, j, and k (some texts write them as ˆ i, ˆ j, and k ˆ ). Information that you may find useful is given on the last page of this exam; you might find it convenient to tear that page off for reference.
1 (10 pts) 1. Someone who was once giving a talk at the Pitt Physics Department said that he planned to speak for about a microcentury. Approximately how many minutes did he plan to speak? Express your answer to the nearest minute. For the purposes of this problem, ignore leap years and take a year to be 365 days. (10 pts) 2. Vector A has a magnitude of 3.0 and points along the positive y-axis, as shown. y A 0 x Vector B has a magnitude of 4.0 and points along the x-axis. (Note that you are not being told in which direction along the axis.) The product B x A points into the page. (5 pts) (a) What is the magnitude of B x A? (2 pts) (b) What is the direction of B? (No explanation is necessary. ) (3 pts) (c) What is the scalar product of A and B?
2 (10 pts) 3. Vectors C and D satisfy the equation 2(C + 3D) = C D. Also, C= 2i j. (5 pts) (a) Find D in terms of i and j. (You may write your answer in terms of fractions.) (5 pts) (b) Find the magnitude and direction of D. Specify the direction by stating the quadrant in which D lies and the angle above or below the x-axis. (15 pts) 4. A ball thrown vertically upward passes by a window. It disappears from the top of the window, and after an interval of 2.0 s it reappears there. Take air resistance on the ball, as well as the size of the ball, to be negligible. (5 pts) (a) How fast (in metric units) was the ball traveling at the instant it disappeared? (5 pts) (b) What was the average velocity of the ball during the 2.0 s interval? (5 pts) (c) What was the average acceleration of the ball during the 2.0 s interval?
3 (15 pts) 5. A projectile is launched with a speed of 24 m/s at an angle of 30 above the horizontal. Take air resistance to be negligible. (5 pts) (a) How long will it take to reach the highest point of its trajectory? (5 pts) (b) What is its velocity there? (5 pts) (c) If it hits the ground at the same vertical level at which it was launched, how far is it from its launching point?
4 (15 pts) 6. N Two bicyclists are riding around a circular track, staying 180 apart. Their speed is 6.0 m/s. At the instant shown in the figure, one is at the north end of the track, heading instantaneously west, and the other is at the south end, heading instantaneously east. The radius of the track is 8.0 m. (5 pts) (a) At the instant shown, what is the acceleration of the cyclist at the north? (5 pts) (b) Is the acceleration constant? Explain briefly. (5 pts) (c) What is the velocity of the north cyclist relative to the south cyclist?
5 (25 pts) 7. A box with a mass of 3.0 kg is on a horizontal plane, and is connected by a cord of negligible mass that passes over a pulley having negligible mass and friction to a box with a mass of 7.0 kg on an inclined plane that makes an angle of 60 with the horizontal. There is negligible friction on the inclined plane, but not on the horizontal plane. The more massive box is sliding down the plane at constant speed. (8 pts) (a) Draw free body diagrams for each of the boxes. Label them clearly. (8 pts) (b) For the less massive box, describe the reaction force whose existence is guaranteed by Newton s third law for each of the forces in your free body diagram. Do so by stating what object exerts the force, what object the force acts on, and how its magnitude compares to that of the force in your diagram. (4 pts) (c) Find the tension in the cord. (5 pts) (d) Find the coefficient of friction.
6 Possibly useful information: v = dr dt, a = dv dt, v = v + at, x x = v t + 1 at 2 0 0 0 2, v 2 = v 2 0 + 2a(x x 0 ), x x 0 = 1 (v + v)t, 2 0 x x 0 = vt 1 at 2 2, a = v2 r, v = v + v P / A P / B B / A, r = xi + yj + zk, a b = abcosφ, a x b = absinφ, g = 9.8 m/s 2 = 32ft/s 2, F = ma, W = mg, f s µ s N, f k = µ k N.