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24 October, 13:07

A. A child is twirling a 1.52 kg object in a vertical circle with a radius of 67.6

cm at constant speed. The tension in the string is 54.7 N at the bottom of

the circle. (a.) What is the speed of the object?

b. (b) What is the tension in the string at the top of the circle?

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Answers (1)
  1. 24 October, 15:59
    0
    (a) 4.21 m/s

    (b) 24.9 N

    Explanation:

    (a) Draw a free body diagram of the object when it is at the bottom of the circle. There are two forces on the object: tension force T pulling up and weight force mg pulling down.

    Sum the forces in the radial (+y) direction:

    ∑F = ma

    T - mg = m v² / r

    v = √ (r (T - mg) / m)

    v = √ (0.676 m (54.7 N - 1.52 kg * 9.8 m/s²) / 1.52 kg)

    v = 4.21 m/s

    (b) Draw a free body diagram of the object when it is at the top of the circle. There are two forces on the object: tension force T pulling down and weight force mg pulling down.

    Sum the forces in the radial (-y) direction:

    ∑F = ma

    T + mg = m v² / r

    T = m v² / r - mg

    T = (1.52 kg) (4.21 m/s) ² / (0.676 m) - (1.52 kg) (9.8 m/s²)

    T = 24.9 N
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