A 21.8 kg beam is attached to a wall with a hinge and its far end is supported b

Question

A 21.8 kg beam is attached to a wall with a hinge and its far end is supported by a cable. The angle between the beam and the cable is 90o. If the beam is inclined at an angle of ? = 27.0

A 21.8 kg beam is attached to a wall with a hinge and its far end is supported by a cable. The angle between the beam and the cable is 90o. If the beam is inclined at an angle of ? = 27.0 degree with respect to horizontal. What is the horizontal component of the force exerted by the hinge on the beam? (Use the `to the right' as + for the horizontal direction.) What is the magnitude of the force that the beam exerts on the hinge?

Explanation / Answer

Resolving mg into two components mg cos ? and mg sin ?,
and since tension T is perpendicular to the beam and since the mg acts at the center of the beam ,
mg cos ? = 2 T and the force on the hinge perpendicular to the beam = T
The force along the beam = mg sin ?
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Answer for a)
mg sin ?* cos ? = 37.4 *9.8 sin 16.5 *cos 16.5=99.8 N

Answer for b)
mg sin ? = 37.4 *9.8 sin 16.5=104.1 N

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