6 - Circular Motion and Other Applications of Newton's Laws

The balls initial velocity is at 480 above the

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Unformatted text preview: h the projectile motion you studied in Chapter 4, but it also moves eastward with the speed you found in part (b). The hole moves to the east at a faster speed, however, pulling ahead of the ball with the relative speed you found in part (c). (d) How far to the west of the hole does the ball land? 66. A car rounds a banked curve as shown in Figure 6.6. The radius of curvature of the road is R, the banking angle is , and the coefficient of static friction is s . (a) Determine the range of speeds the car can have without slipping up or down the banked surface. (b) Find the minimum value for s such that the minimum speed is zero. (c) What is the range of speeds possible if R 100 m, 10.0°, and s 0.100 (slippery conditions)? 67. A single bead can slide with negligible friction on a wire that is bent into a circle of radius 15.0 cm, as in Figure P6.67. The circle is always in a vertical plane and rotates steadily about its vertical diameter with a period of 0.450 s. The position of the bead is described by the angle that the radial line from the center of the loop to the bead makes with the vertical. (a) At what angle up from the lowest point can the bead stay motionless relative to the turning circle? (b) Repeat the problem if the period of the circle’s rotation is 0.850 s. θ Golf ball trajectory R E cos φ i φi Figure P6.67 Figure P6.64 65. A curve in a road forms part of a horizontal circle. As a car goes around it at constant speed 14.0 m/s, the total force exerted on the driver has magnitude 130 N. What are the magnitude and direction of the total force exerted on the driver if the speed is 18.0 m/s instead? 68. The expression F arv br 2v 2 gives the magnitude of the resistive force (in newtons) exerted on a sphere of radius r (in meters) by a stream of air moving at speed v (in meters per second), where a and b are constants with appropriate SI units. Their numerical values are a 3.10 10 4 and b 0.870. Using this formula, find the terminal speed for water droplets falling under their own weight in air, taking the following values for the drop radii: (a) 10.0 m, (b) 100 m, (c) 1.00 mm. Note that for (a) and (c) you can obtain accurate answers without solving a quadratic equation, by considering which of the two contributions to the air resistance is dominant and ignoring the lesser contribution. 69. A model airplane of mass 0.750 kg flies in a horizontal circle at the end of a 60.0-m control wire, with a speed of 35.0 m/s. Compute the tension in the wire if it makes a constant angle of 20.0° with the horizontal. The forces exerted on the airplane are the pull of the control wire, 181 Answers to Quick Quizzes its own weight, and aerodynamic lift, which acts at 20.0° inward from the vertical as shown in Figure P6.69. Flift 20.0° stable spread position” versus the time of fall t. (a) Convert the distances in feet into meters. (b) Graph d (in meters) versus t. (c) Determine the value of the terminal speed vt by finding the slope of the s...
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