A juggler has three objects in the air simultaneously. The masses of the objects are m, 2m, and 3m. At a particular instant, their respectiv

Question

A juggler has three objects in the air simultaneously. The masses of the objects are m, 2m, and 3m. At a particular instant, their respective vertical velocities are v, 0, and -v, where positive velocity is upward.1) What is the magnitude of the acceleration of the centre of mass of the three-object system at this instant?a) zerob) g/3c) g/2d) ge) g/6

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Thu Thảo 1 week 2021-07-21T22:15:04+00:00 1 Answers 1 views 0

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    2021-07-21T22:16:11+00:00

    Answer:

    the result  a_{cm} = g   .The correct answer is d

    Explanation:

    For this problem let’s start by finding the center of mass of objects

             x_{cm} = 1 / M ∑ x_{i}  m_{i}

    we apply this equation to our case

            M = m + 2m + 3m

           M = 6m

            x_{cm} = 1 / 6m (x₁ m + x₂ 2m + x₃ 3m)

            x_{cm} = 1/6 (x₁ + 2 x₂ + 3x₃)

    We apply Newton’s second law to this center of mass

             dp / dt = M a

             d (M v_{cm}) / dt = M a

    let’s find the speed of the center of mass

            v_{cm} = 1 / 6m (m v + 2m 0 – 3m v)

            v_{cm} = ⅓ v

             M d v_{cm}/ dt = M a

             d v_{cm} / dt = a

    at the center of mass the external force of the system is applied, which is the force of gravity

             dv_{cm} / dt = g

    therefore the result

                   a = g

     

    The correct answer is d

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