A pendulum consists of a 4.0 kg stone swinging on a 4.4 m string of negligible m

Question

A pendulum consists of a 4.0 kg stone swinging on a 4.4 m string of negligible mass. The stone has a speed of 7.5 m/s when it passes its lowest point. (a) What is the speed when the string is at 60 ? to the vertical? (b) What is the greatest angle with the vertical that the string will reach during the stone's motion? (c) If the potential energy of the pendulum-Earth system is taken to be zero at the stone's lowest point, what is the total mechanical energy of the system?

(a) Number Unit m/s
(b) Number Unit degrees
(c) Number Unit J

Explanation / Answer

a) dh = L(1-cos60°) = 4.2*(1 - cos60) = 2.1 m. V60 = v[Vmax² - 2g*dh] = 3.88 m/s b) dhmax = Vmax²/2g = 2.87 m. T = arccos[(L - dhmax)/L] = 71.54° c) Etot = KEmax = ½m*Vmax² = 56.25 J

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