Chapter 5 – part B. Non uniform circular motion Velocity dependent resistive forces. Exercise 5.20.
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Non uniform circular motion
Velocity dependent resistive forces
20. A 4.00-kg object is attached to a vertical rod by two strings as shown in Figure P5.20. The object rotates in a horizontal circle at constant speed 6.00 m/s. Find the tension in (a) the upper string and (b) the lower string.
47. In a home laundry dryer, a cylindrical tub containing wet clothes is rotated steadily about a horizontal axis as shown in Figure P5.47. The clothes are made to tumble so that they will dry uniformly. The rate of rotation of the smooth-walled tub is chosen so that a small piece of cloth will lose contact with the tub when the cloth is at an angle of 68.0° above the horizontal. If the radius of the tub is 0.330 m, what rate of revolution is needed?
50. An air puck of mass m1 is tied to a string and allowed to revolve in a circle of radius R on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a counterweight of mass m2 is tied to it (Fig. P5.50). The suspended object remains in equilibrium while the puck on the tabletop revolves. What are (a) the tension in the string, (b) the radial force acting on the puck, and (c) the speed of the puck?
28. A 9.00-kg object starting from rest falls through a viscous medium and experiences a resistive force where is the velocity of the object. The object reaches one-half its terminal speed in 5.54 s. (a) Determine the terminal speed. (b) At what time is the speed of the object three-fourths the terminal speed? (c) How far has the object traveled in the first 5.54 s of motion?
30. Consider an object on which the net force is a resistive force proportional to the square of its speed. For example, assume that the resistive force acting on a speed skater is f = –kmv2, where k is a constant and m is the skater’s mass. The skater crosses the finish line of a straight-line race with speed v0 and then slows down by coasting on his skates. Show that the skater’s speed at any time t after crossing the finish line is v(t) = v0/(1 + ktv0).