Calculate the net torque (magnitude and direction) on the beam in the figure bel

Question

Calculate the net torque (magnitude and direction) on the beam in the figure below about the following axes. (Assume = 49°, = 27°, = 17°, = 4.4 m)

(a) an axis through O perpendicular to the page

magnitude= N · m

direction

(b) an axis through C perpendicular to the page

magnitude= N · m

direction

2. One end of a uniform 4.30-m-long rod of weight Fg is supported by a cable at an angle of = 37° with the rod. The other end rests against the wall, where it is held by friction as shown in the figure below. The coefficient of static friction between the wall and the rod is s = 0.470. Determine the minimum distance x from point A at which an additional object, also with the same weight Fg, can be hung without causing the rod to slip at point A.

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Explanation / Answer

1) Torque about an axis through O perpendicular to the page,

T_O = 25*(l/2)*sin(90+beta) - 10*l*sin(gamma)

= (25*(4.4/2)*sin(90+27) - 10*4.4*sin(17)

= 36.1 N.m

direction : counterclockwise

b)

Torque about an axis through C perpendicular to the page,

T_C = 30*(l/2)*sin(alfa) - 10*(l/2)*sin(gamma)

= 30*(4.4/2)*sin(49) - 10*(4.4/2)*sin(17)

= 43.3 N.m

direction : counterclockwise

2) Figure is missing.

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