A small 0.18 kg metal ball is tied to a very light (essentially massless) string that is 0.8 m long. The string is attached to the ceiling so as to form a pendulum. The pendulum is set into motion by releasing it from rest at an angle of 40 ∘ with the vertical.

What is the speed of the ball when it reaches the bottom of the arc? What is the centripetal acceleration of the ball at this point?What is the tension in the string at this point?

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  1. height above bottom at 40deg
    h = .8(1-cos 40)
    compute h

    potential energy at that height
    U = m g h = .18*9.81*h
    compute U

    kinetic energy at bottom Ke = (1/2)m v^2 = U
    compute v

    Ac = v^2/R = v^2/.8
    compute Ac

    T = m g + m Ac

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