You slip a wrench over a bolt. Taking the origin at the bolt, the other end of the wrench is at x=18cm, y=5.5cm. You apply a force F? =88i^?

Question

You slip a wrench over a bolt. Taking the origin at the bolt, the other end of the wrench is at x=18cm, y=5.5cm. You apply a force F? =88i^?23j^ to the end of the wrench. What is the torque on the bolt?

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Thu Giang 5 years 2021-08-10T07:28:52+00:00 1 Answers 113 views 0

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  1. bonexptip
    0
    2021-08-10T07:30:17+00:00
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    Answer:

    The torque on the wrench is 4.188 Nm

    Explanation:

    Let r = xi + yj where is the distance of the applied force to the origin.

    Since x = 18 cm = 0.18 cm and y = 5.5 cm = 0.055 cm,

    r = 0.18i + 0.055j

    The applied force f = 88i – 23j

    The torque τ = r × F

    So, τ = r × F = (0.18i + 0.055j) × (88i – 23j) = 0.18i × 88i + 0.18i × -23j + 0.055j × 88i + 0.055j × -23j

    = (0.18 × 88)i × i + (0.18 × -23)i × j + (0.055 × 88)j × i + (0.055 × -22)j × j  

    = (0.18 × 88) × 0 + (0.18 × -23) × k + (0.055 × 88) × (-k) + (0.055 × -22) × 0   since i × i = 0, j × j = 0, i × j = k and j × i = -k

    = 0 – 4.14k + 0.0484(-k) + 0

    = -4.14k – 0.0484k

    = -4.1884k Nm

    ≅ -4.188k Nm

    So, the torque on the wrench is 4.188 Nm

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