A bucket of water of mass 20 kg is pulled at constant velocity up to a platform 35 meters above the ground. This takes 14 minutes, during wh

Question

A bucket of water of mass 20 kg is pulled at constant velocity up to a platform 35 meters above the ground. This takes 14 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. (Use .)

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Thiên Hương 4 years 2021-08-09T10:59:17+00:00 1 Answers 38 views 0

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  1. thuthuy
    0
    2021-08-09T11:00:20+00:00
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    Answer:

    5831J

    Explanation:

    Data;

    Mass of water = 20kg

    Height = 35m

    Time = 14minutes

    Mass if leakage = 6kg

    g = 9.8 m

    The bucket moves upward 35/14m/min at time t,

    The height of the bucket =

    y = (35 / 14)t metres above the ground.

    Water drips out at the rate of 6kg/ 14mins

    At first, there was 20kg of water in the bucket, at time t, the mass remaining = ?

    M = (20 – 6/14)t kg

    Consider the time interval between t and t + ∇t. During this time, the bucket moves a distance of

    ∇y = (35/14 ∇t) J

    W = lim ₓ→ₐ ∑ (20 -3/7)t *g* 35/14 ∇t

    W = ∫¹⁴₀ (20-3/7)t * g * 35/14 dt

    W = 35/14g (20t – 3/14t²) |¹⁴

    W = 35/14g [20(14) – 3/14(14)²]

    W = 35/14*g* (280-42)

    W = 5831J

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