Three friends tie three ropes in a knot and pull on the ropes in different directions. Adrienne (rope 1) exerts a 20-N force in the positive

Question

Three friends tie three ropes in a knot and pull on the ropes in different directions. Adrienne (rope 1) exerts a 20-N force in the positive x-direction, and Jim (rope 2) exerts a 40-N force at an angle 53∘ above the negative x-axis. Luis (rope 3) exerts a force that balances the first two so that the knot does not move.
a. Use equilibrium conditions to find F LonKx and F LonKy.
b. Use equilibrium conditions to determine the magnitude of F⃗ LonK.
c. Use equilibrium conditions to determine the angle θ that describes the direction of F⃗ LonK. Use positive values if the force is directed above the positive x-axis and negative values if it is directed below the positive x-axis.
d. Construct a force diagram for the knot.

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Diễm Kiều 3 weeks 2021-08-23T23:02:02+00:00 1 Answers 0 views 0

Answers ( )

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    2021-08-23T23:03:58+00:00

    Answer:

    Part a)

    F = 4 \hat i - 32\hat j

    Part b)

    Magnitude of the force is given as

    F = 32.2 N

    Part c)

    As we know that Y component of the force is negative so here the force is directed below the X axis

    \theta = -82.9 degree

    Explanation:

    Part a)

    Adrienne apply the force of 20 N along +X direction and Jim apply force of 40 N at 53 degree above negative X axis

    so we will have

    F_1 = 20 \hat i

    F_2 = 40cos53(-\hat i) + 40 sin53(\hat j)

    F_2 = -24\hat i + 32\hat j

    now let say the force exerted by Luis is F such that sum of all forces must be zero

    now we have

    F_1 + F_2 + F_3 = 0

    so we have

    20\hat i -24\hat i + 32\hat j + F = 0

    -4\hat i + 32\hat j + F = 0

    F = 4 \hat i - 32\hat j

    Part b)

    Magnitude of the force is given as

    F = \sqrt{4^2 + 32^2}

    F = 32.2 N

    Part c)

    As we know that Y component of the force is negative so here the force is directed below the X axis

    So here we have

    tan\theta = -\frac{32}{4}

    \theta = -82.9 degree

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