A child on a tricycle is moving at a speed of 1.40 m/s at the start of a 2.25 m high and 12.4 m long incline. The total mass is 48.0 kg, air

Question

A child on a tricycle is moving at a speed of 1.40 m/s at the start of a 2.25 m high and 12.4 m long incline. The total mass is 48.0 kg, air resistance and rolling resistance can be modeled as a constant friction force of 41.0 N, and the speed at the lower end of the incline is 6.50 m/s. Determine the work done (in J) by the child as the tricycle travels down the incline.

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Sapo 5 years 2021-07-17T16:56:54+00:00 1 Answers 130 views 0

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  1. King
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    2021-07-17T16:58:08+00:00
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    Answer:

    The work done by the child as the tricycle travels down the incline is 416.96 J

    Explanation:

    Given;

    initial velocity of the child, v_i = 1.4 m/s

    final velocity of the child, v_f = 6.5 m/s

    initial height of the inclined plane, h = 2.25 m

    length of the inclined plane, L = 12.4 m

    total mass, m = 48 kg

    frictional force, f_k = 41 N

    The work done by the child is calculated as;

    \Delta E_{mech} = W - f_{k} \Delta L\\\\W = \Delta E_{mech} + f_{k} \Delta L\\\\W = (K.E_f - K.E_i) + (P.E_f - P.E_i) + f_{k} \Delta L\\\\W = \frac{1}{2} m(v_f^2 - v_i^2) + mg(h_f - h_i) + f_{k} \Delta L\\\\W = \frac{1}{2} \times 48(6.5^2 - 1.4^2) + 48\times 9.8(0-2.25) + (41\times 12.4)\\\\W = 966.96 \ - \ 1058.4 \ + \ 508.4\\\\W = 416.96 \ J

    Therefore, the work done by the child as the tricycle travels down the incline is 416.96 J

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