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A 3 m long pole lies along the x-axis with one end at
the origin. At the other end (point A), a rope is
attached and guyed back to a point on the wall
(point B), located at (0,1.2,-2) (in m). The tension in
the rope is 2500 N. Replace the force applied by the
rope on the pole by an equivalent force couple
system located at the origin. What is the z-component of the required moment?

A 3 m long pole lies along the xaxis with one end at the origin At the other end point A a rope is attached and guyed back to a point on the wall point B locate class=

Respuesta :

onyebuchinnaji

The z-component of the required moment is -3947.36 Nm.

The given parameters;

  • length of the pole, L = 3 m
  • tension in the rope, T = 2,500 N

A little sketch of the given problem is presented below;

     B  ↑ (0, 1.2, -2)

          ↑

          ↑

(0, 0, 0) -------------------------(3, 0, 0) A

The force couple system located at the origin is calculated as;

τ = FL

τ = 2500 x 3

τ = 7500 N.m

The resultant of the coordinate vectors is calculated as;

[tex]r = 3i + 1.2j -2k\\\\|r| = \sqrt{3^2 + 1.2^2 + (-2)^2} \\\\|r| = 3.8[/tex]

The z-component of the required moment is calculated as;

[tex]\tau = 7500 \times \frac{3i \ +\ 1.2j \ -2k\ }{3.8} \\\\\tau = 1973.68(3i \ +\ 1.2j \ -2k\ )\\\\\tau = (5921.04 i \ + \ 2,368.41j \ - \ 3947.36 k)\ Nm[/tex]

Thus, the z-component of the required moment is -3947.36 Nm.

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