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11 January, 00:04

How fast do you need to swing a 190-g ball at the end of a string in a horizontal circle of 0.50-m radius so that the string makes a 38 ∘ angle relative to the horizontal?

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  1. 11 January, 00:12
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    The speed you need to swing the ball at the end of the string in a horizontal circle is 2.504 m/s

    Explanation:

    As the ball swings, its motion creates tension (T) on the string which has both vertical component and horizontal component.

    Vertical or Y-component: The tension on the string is equal to down ward force on the ball due to gravity.

    Tsin38⁰ = mg

    Tsin38⁰ = 0.19 x 9.8

    Tsin38⁰ = 1.862

    T = (1.862) / (0.6157)

    T = 3.024 N

    Horizontal or X-component: The tension on the string is equal to centripetal force on the ball which acts inward.

    Tcos38⁰ = m (v²/r)

    3.024 (0.78801) = 0.19 (v²/0.5)

    2.3829 = 0.38*v²

    v² = 2.3829 / 0.38

    v² = 6.2708

    v = √6.2708

    v = 2.504 m/s

    Therefore, the speed you need to swing the ball at the end of the string in a horizontal circle is 2.504 m/s
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