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27 February, 21:31

A soccer player extends her lower leg in a kicking motion by exerting a force with the muscle above the knee in the front of her leg. she produces an angular acceleration of 37.5 rad/s2 and her lower leg has a moment of inertia of 0.750 kg · m2. what is the force exerted by the muscle, in newtons, if its effective perpendicular lever arm is 3.30 cm?

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Answers (2)
  1. 27 February, 22:25
    0
    The force exerted by the muscle is 852.27N

    Explanation:

    Force F exerted by the muscle is expressed as a function of the torque τ and the effective perpendicular arm r.

    F = τ/r ... (1)

    Where τ = moment of inertia I * angular acceleration α

    τ = Iα ... (2)

    Substituting equation 2 into 1 to get F will give;

    F = Iα/r

    Given the following parameters

    I = 0.75kgm²

    α = 37.5rad/s²

    r = 3.30cm = 0.033m

    F = 0.75 (37.5) / 0.033

    F = 28.125/0.033

    F = 852.27N

    The force exerted by the muscle is 852.27N
  2. 28 February, 00:27
    0
    Force exerted by muscle = 852.27N

    Explanation:

    We are given that;

    lever arm; d = 3.3cm = 0.033m

    Angular acceleration; α = 37.5 rad/s²

    Moment of inertia of Leg; I = 0.75 kg. m²

    Now, we know that torque is given by the relationship;

    τ = Iα

    Where, I is moment of inertia and α is angular acceleration.

    Thus,

    τ = 0.75 x 37.5 = 28.125 N. m

    Now, the relationship between torque and force is given by;

    Torque = Force x perpendicular distance

    We have torque = 28.125 N. m

    We also have perpendicular distance as the lever arm = 0.033m

    Thus,

    28.125 N. m = Force x 0.033m

    Thus,

    Force = 28.125 N. m/0.033m

    Force = 852.27N
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