ADDITIONS TO WOLFSON PROBLEMS AND PROBLEMS FROM OTHER TEXTS MAY 31 - JUNE 6 WOLFSON CHAPTER 3 21. (c) Also find the solution graphically. (d) If your walking speed was a constant 1 km/hr, what was your average velocity after completing the first two legs of the trip. 55. Assume the clock is a wall clock and you are facing it. Take the time interval as starting at 12.5 s and ending at 17.5 s. In (a) and (b) give not only the magnitude of the vectors but also the direction. FISHBANE - CHAPTER 2 22. Inclined planes are convenient tools to study motion under a constant acceleration. The time of passage of a ball rolling on an inclined plane is measured by three light gates positioned 60 cm apart. The ball passes the light gates at 0.30 s, 1.15 s, and 1.70 s. Find the acceleration of the ball. HALLIDAY AND RESNICK - 2ND Ed. - CHAPTER 2 65. A drowsy cat spots a flowerpot that sails first up and then down past an open window. The pot is in view for a total of 0.50 s, and the top-to-bottom height of the window is 2.00 m. How high above the window top does the flowerpot go? HALLIDAY AND RESNICK - 2ND Ed. - CHAPTER 3 6. A particle had a velocity of 18 m/s and 2.4 s later its velocity was 30 m/s in the opposite direction. What was the average acceleration of the particle during this 2.4 s interval? 39. The position of a particle moving along the x axis is given in centimeters by x = 9.75 + 1.50(t^3), where t is in seconds. Consider the time interval t=2 s to t=3 s and calculate (a) the average velocity; (b) the instantaneous velocity at t=2 s; (c) the instantaneous velocity at t=3 s; (d) the instantaneous velocity at t=2.5 s; (e) the instantaneous velocity when the particle is midway between its positions at t=2 s and t=3 s. (f) Graph x vs t and indicate your answers graphically. (g) Find the acceleration of the particle at t = 10 s. FISHBANE - CHAPTER 3 14. A particle moves in such a way that its coordinates are x(t) = (A)cos(wt) and y(t) = (A)sin(wt), where "w" stands for the Greek letter omega. Calculate the x- and y-components of the velocity and the acceleration of the particle. 28. A man in the crow's nest of a sailing ship moving through smooth seas at a steady 12 km/h accidentally lets a cannonball drop from his station, which is 8.5 m above the deck at the top of the mainmast. (a) Assuming that he dropped the ball from a position immediately adjacent to the vertical mast, where does the ball land with respect to the mast? (b) How long does it take for the ball to fall to the deck? (c) In the time it takes the ball to fall, what is the magnitude of the displacement of the ball as measured by the fixed observer? 60. An airplane is to fly due north from New Orleans to St. Louis, a distance of 673 mi. On that day and at the altitude of the flight, a wind blows from the west at a steady speed of 65 mi/h. The airplane can maintain an air speed of 180 mi/h. Ignore the periods of takeoff and landing. (a) In what direction must the airplane fly in order to arrive at St. Louis without changing direction? Draw a diagram and label this direction with an angle. Would this calculation change if the distance between the cities were twice as great? (b) What is the flying time for this flight? (c) Recalculate the flying time if the airplane heads due north until it reaches the latitude of St. Louis, and then flies due west, into the wind to reach the city. 65. A boat is required to traverse a river that is 150 m wide. The current in the river moves with a speed of 6 km/h. The boat can be rowed on still water with a speed of 10 km/h. Set up a convenient coordinate system in which to describe the various displacements. Using this coordinate system, write down the position vector of the boat at time t, assuming that the boat moves with uniform speed and that it leaves one side with the velocity vector making an angle theta with the direction of the river. Calculate theta such that the boat lands at a point exactly opposite the starting point. How long will the trip take? SERWAY - CHAPTER 3 62. After delivering his toys in the usual manner, Santa decides to have some fun and slide down an icy roof. The roof is 8 m in length and makes an angle of 37 degrees with the horizontal. He starts from rest at the top of the roof and accelerates at the rate of 5 m/s^2. The edge of the roof is 6 m above a soft snowbank, on which Santa lands. Find (a) Santa's velocity components when he reaches the snowbank, (b) the total time he is in motion, and (c) the horizontal distance d between the house and the point where he lands in the snow. FISHBANE - CHAPTER 4 24. (The figure for this problem is Wolfson Fig. 5-36, on page 118. Only the numbers are different.) Part I: A force of magnitude 8.0 N pushes on a horizontally stacked set of blocks on a frictionless surface with masses m1 = 2.0 kg, m2 = 3.0 kg, and m3 = 4.0 kg. (a) What is the acceleration of the stack? (b) What are the horizontal forces on block 1, as well as the net force on this block. (c) Repeat part b for block 2. (d) Repeat part b for block 3. Part II: Repeat Part I, but this time with the blocks stacked in reverse order; that is, block 3 to the left and block 1 to the right. The 8.0 N force is still pushing from the left (so it is now pushing on block 3). HALLIDAY AND RESNICK - 2ND Ed. - CHAPTER 5 14. A 29.0 kg child, with a 4.50 kg backpack on his back, first stands on a sidewalk and then jumps up into the air. Find the magnitude and direction of the force on the sidewalk from the child when the child is (a) standing still and (b) in the air. Now find the magnitude and direction of the net force ON the Earth due to the child when the child is (c) standing still and (d) in the air. (Note: the sidewalk is a part of the Earth.) FBD's are required in your work for this problem. 27. A firefighter with a weight of 712 N slides down a vertical pole with an acceleration of 3.00 m/s^2, directed downward. What are the magnitudes and directions of the vertical forces (a) on the firefighter by the pole and (b) on the pole by the firefighter? FBD's are required in your work for this problem. 50. The figure below shows a man sitting in a bosun's chair that dangles from a massless rope, which runs over a massless, frictionless pulley and back down to the man's hand. The combined mass of man and chair is 95.0 kg. WIth what force magnitude must the man pull on the rope is he is to rise (a) with a constant velocity and (b) with an upward acceleration of 1.30 m/s^2. Suppose, instead, that the rope on the right extends to the ground, where it is pulled by a co-worker. With what force magnitude must the co-worker pull for the man to rise (c) with a constant velocity and (d) with an upward acceleration of 1.30 m/s^2. What is the magnitude of the force on the ceiling from the pulley system in (e) part a, (f) part b, (g) part c, and (h) part d? figure gif version pdf version