<p>A simple pendulum, which you will consider in detail in Chapter 12, consists

Question

<p>A simple pendulum, which you will consider in detail in Chapter 12, consists of an object suspended by a string. The object is assumed to be a particle. The string, with its top end fixed, has negligible mass and does not stretch. In the absence of air friction, the system oscillates by swinging back and forth in a vertical plane. The string is 2.00 m long and makes an initial angle of 30.0&#176; with the vertical. &#160;Calculate the speed of the particle (a) at the lowest point in its trajectory and (b) when the angle is 15.0&#176;.</p>

Explanation / Answer

we have, from work energy theorem, 0 - 0.5mv^2 = -mgL(1-cos(30)) v^2 = 2 x 9.8 x 2 (1-cos(30)) Speed = v = 2.292 m/s a. Speed at bottom = v = 2.292 m/s b. 0.5mv'^2-0.5mv^2 = -mgL(1-cos(15)) v'^2 - 2.292^2 = -2 x 9.8 x 2 (1-cos(15)) Speed = v' = 1.979 m/s

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