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March 24, 2017

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A tether ball of mass 0.25 kg is attached to a vertical pole by a cord 1.4 m long. Assume the cord attaches to the center of the ball. The cord makes an angle of 20° with the vertical.

(a) What is the tension in the cord?

(b) What is the speed of the ball?

  • Physics - ,

    r = radius of circle = 1.4 sin 20
    centripetal acceleration = v^2/r
    horizontal force needed = m v^2/r
    but
    horizontal component of tension = T sin 20
    vertical component of tension = T cos 20 = m g
    so
    T = m g/cos 20 = 2.61 Newtons (part A)

    so
    T sin 20 = m v^2/r = m v^2/1.4 sin 20
    2.61 (1.4 )sin^2 20 = .25 v^2
    solve for v

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