A bucket of water of mass 20 kg is pulled at constant velocity up to a platform 32 meters above the ground. This takes 8 minutes, during whi

Question

A bucket of water of mass 20 kg is pulled at constant velocity up to a platform 32 meters above the ground. This takes 8 minutes, during which time 6 kg of water drips out at a steady rate through a hole in the bottom. Find the work needed to raise the bucket to the platform. Assume g

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Thu Nguyệt 6 months 2021-07-31T12:30:17+00:00 1 Answers 3 views 0

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    2021-07-31T12:31:19+00:00

    Answer:

    W=-1881.6J

    Explanation:

    we have that the change in the mass is

    \frac{dm}{dt}=-c\\m(0)=60kg\\m(8)=60kg-6kg=54kg

    by solving the differential equation and applying the initial conditions we have

    \int dm=-c\int dt\\m=-ct+d\\m(0)=-c(0) + d=60 \\m(8)=-8c+d=54

    by solving for c and d

    d=60

    c=0.75

    The work needed is

    W = m(t) gh

    by integrating we have

    dW_T= gh\int dm \\\\W_T=gh\int_0^8 -0.75dt\\\\W_T=(9.8\frac{m}{s^2})(32m)(-0.75(8))=-1881.6J

    hope this helps!!

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