A very slippery ice cube slides in a vertical plane around the inside of a smooth, 20-cm-diameter horizontal pipe. The ice cube’s speed at t

Question

A very slippery ice cube slides in a vertical plane around the inside of a smooth, 20-cm-diameter horizontal pipe. The ice cube’s speed at the bottom of the circle is 3.0 m/s. What is the ice cube’s speed at the top?

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Adela 1 year 2021-07-27T15:59:06+00:00 1 Answers 193 views 0

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    2021-07-27T16:00:33+00:00

    Answer:

    Explanation:

    Given that,

    Diameter of pipe

    d = 20cm

    Then, radius =d/2 =20/2

    r = 10cm =0.1m

    The speed at the bottom is

    Vi = 3m/s

    Speed at the top Vf?

    At the bottom the cube is at a height of 0m

    Then, y1 = 0m

    At the top the cube is at a height which is the same as the diameter of the pipe

    y2 = 0.2m

    Now, let us consider, the energy conservation equation , which is the sum of kinetic energy and gravitational potential energy, given by,

    K2 + U2 = K1 + U1

    ½m•Vf² + m•g•y2 = ½m•Vi² + m•g•y1

    Divide all through by m

    ½•Vf² + g•y2 = ½•Vi² + g•y1

    Since y1 = 0

    So we have,

    ½•Vf² + g•y2 = ½•Vi²

    ½•Vf² = ½•Vi² — g•y2

    Multiply through by 2

    Vf² = Vi² —2g•y2

    Vf = √(Vi²—2g•y2)

    g is a constant =9.81m/s2

    Vf = √(3²—2×9.81×0.2)

    Vf = √(9—0.981)

    Vf = √8.019

    Vf = 2.83m/s

    The speed of the ice cubes at the top of the pipe is 2.83m/s

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