Some gliders are launched from the ground by means of a winch, which rapidly reels in a towing cable attached to the glider. What average po

Question

Some gliders are launched from the ground by means of a winch, which rapidly reels in a towing cable attached to the glider. What average power must the winch supply in order to accelerate a 156-kg ultralight glider from rest to 24.9 m/s over a horizontal distance of 58.0 m? Assume that friction and air resistance are negligible, and that the tension in the winch cable is constant.

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King 6 months 2021-08-04T10:30:49+00:00 1 Answers 17 views 0

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    2021-08-04T10:32:26+00:00

    Answer:

    P=627.47W

    Explanation:

    To solve this problem we have to take into account, that the work done by the winch is

    W=Fh

    the force, at least must equal the gravitational force

    F=Mg=(156kg)(9.8\frac{m}{s^2})=1258.8N

    with force the tension in the cable makes the winch go up.

    The work done is

    W=(1258.8N)(58.0m)=73010.4J

    To calculate the power we need to know what is the time t. But first we have to compute the acceleration

    The acceleration will be

    v_f^2=v_0+2ah\\a=\frac{v_f^2}{2h}=\frac{(24.9\frac{m}{s})}{2(58.0m)}=0.214\frac{m}{s^2}

    and the time t

    v_f=v_0+at\\t=\frac{v_f}{a}=116.35s

    The power will be

    P=\frac{W}{t}=\frac{73010.4J}{116.35s}=627.47W

    HOPE THIS HELPS!!

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