A baton twirler in a marching band competition grabs one end of her 1.2 kg, 1.0 meter long baton. She throws her baton into the air such tha

Question

A baton twirler in a marching band competition grabs one end of her 1.2 kg, 1.0 meter long baton. She throws her baton into the air such that it rises to a height of 5.0 meters while spinning end over end at a rate of 3.5 revolutions per second. How much work did she do on the baton?

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Farah 4 years 2021-09-02T18:50:46+00:00 1 Answers 17 views 0

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  1. Ladonna
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    2021-09-02T18:51:46+00:00
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    Answer:

    349 J

    Explanation:

    Length L of baton = 1.0 m

    Mass m of baton = 1.2 kg

    Weight W of baton = 1.2 kg x 9.81 m/s^{2} = 11.772 N

    Height h reached = 5.0 m

    Angular speed ω = 3.5 rev/s = 2π x 3.5 (rad/s) = 21.99 rad/s

    Total work done on baton will be the work done in taking it to a height of 5.0 m and the kinetic energy with which the baton rolls.

    Work done to bringing it to the height of 5.0 m = weight x height above ground

    W x h = 11.772 x 5 = 58.86 J

    Velocity v of spinning baton = ω x L = 21.99 x 1 = 21.99 m/s

    Kinetic energy = \frac{1}{2}mv^{2} =

    Total work done on baton = 58.86 + 290.14 = 349 J

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