CLASSICAL MECHANICS & THERMODYNAMICS - Chapter 5, Exercise 1 Solution
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Centripetal Force on a Ball Swung on a String

PROBLEM
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A 0.3 kg ball is swung in a horizontal circle on a 1.2 m string at a
constant speed of 6 m/s. Calculate the centripetal force the string
must provide.

SOLUTION
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Using the centripetal force formula:

    F_c = m v^2 / r

Substitute the given values:

    m = 0.3 kg
    v = 6 m/s
    r = 1.2 m

    F_c = 0.3 x 6^2 / 1.2
    F_c = 0.3 x 36 / 1.2
    F_c = 10.8 / 1.2
    F_c = 9 N

ANSWER: The string must provide a centripetal force of 9 N.

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WHY THIS WORKS AS AN ANSWER

The ball is moving at constant speed but constantly changing
direction, which (per Chapter 2's own Second Law) requires a
continuous net inward force - here supplied entirely by the tension
in the string, which always pulls toward the centre of the circle the
ball traces out. If the string could not supply at least 9 N of
tension, it would break and the ball would fly off in a straight line
tangent to the circle at the moment of release, exactly as Newton's
First Law predicts for an object with no net force acting on it.