Imagine you swing a 2 meter long pendulum with a mass of 10kg. Letthe point at w

Question

Imagine you swing a 2 meter long pendulum with a mass of 10kg. Letthe point
at which the pendulum is hanging straight down be the zero pointfor the potential energy. For fun you pull the pendulum back anangle of 32 degrees from the vertical and release it from rest.

a. Find the initial kinetic and potential energy of the pendulum atthe moment just before you release it. (3 points)

b. Find the velocity of the pendulum at its lowest point of swing.(2 points)

c. Find the maximum height that the pendulum will swing to on theother side. (2 points)

Explanation / Answer

height of the pendulum is        h = L (1 - cos )           = 2 (1- cos 32)           = 0.3mfrom the ground.
a) The inital kinetic energy is zero. The initla potentialenergy is        U = mg h            =(10)(9.8)(0.3)            =29.4J b) from energy conservation        (1/2)mv2 = m gh       (1/2)mv2 = 29.4 J                 v = [2 x 29.4 / m ] Speed at the bottom            v= 2.425m/s c) again energy conservation         m g h' = (1/2)mv2                   = 29.4                     h ' = 0.3 m              =        

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