A 2-kg stone attached to a string is whirled in a horizontal circle of radius 40

Question

A 2-kg stone attached to a string is whirled in a horizontal circle of radius 40 cm (like the tetherball in Figure 5-26). The string makes an angle of 30" with the vertical. Find the tension in the string and the speed of the stone. A model airplane of mass 500 g flies in a horizontal circle of radius 6 m attached to a horizontal string. (The weight of the plane is balanced by the upward "lift" force of the air on the wings of the plane.) The plane makes 1 rev every 4 s. What is the speed of the plane? What is the acceleration of the plane? What is the tension in the string? A penny is placed on a record that is gradually accelerated to 78 rev/min. The penny stays on the record if it is placed within 8 cm of the center but slides off if it is placed farther from the center. What is the coefficient of friction between the penny and the record?

Explanation / Answer

Data: Mass, m = 0.5 kg Radius, r = 6 m Angular velocity, = (1 / 4) rev/s                               = 0.25 * 2 rad/s                               = 0.5 rad/s (a) Speed of the aeroplane, v = r                                         = 6 * 0.5                                         = 9.42 m/s Ans: Speed of the aeroplane, v = 9.42 m/s (b) Aceleration of the plane, a = v^2 / r                                          = 9.42^2 / 6                                          = 14.8 m/s^2 Ans: Acceleration of the plane, a = 14.8 m/s^2 (c) Tension in the string, T = Centripetal force                                    = m v^2 / r                                    = 0.5 * 9.42^2 / 6                                    = 7.4 N Ans: Tension, T = 7.4 N

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