a light cable is used to support a beam of mass 80kg and a metal sphere of mass

Question

a light cable is used to support a beam of mass 80kg and a metal sphere of mass 200 kg. The beam is perpendicular to a wall. The length of the beam is 2m. the cable supporting the beam is holding the beam at 1m on the beam. The angel between the wall and the place where the cable is attached to the wall is 40 degree. A 200 gram sphere is on the opposite end of the beam from the wall. (a) draw a diagram of all the forces acting on the beam (b) find the tension in the cable (c) find the horizontal and vertical components of the force of the wall on beam .

Explanation / Answer

Let O be the point at which the beam ,wire and the load meet . Construct the x- y coordinate axes with O as the origin. The magnitude of the tension in the wire be T and it is at an angle 40 to the horizontal at the point of suspension of the load and toward the wall. The magnitude of the tension in the rod be R and is at angle 40 to the horizontal at the point of suspension of the load and away from the wall. T sin 40 + R sin 40 = 1955 T sin 50 + = 1955- R sin 30 Also T cos 50 = R cos 30 Dividing tan 50 = (1955/R cos 30) - tan 30 Solving R = 1276.04 N and T = 1719.2 N Answer T = 1719.2 N ==================== Horizontal component R cos 30 =1276.04 cos 30 = 1105.08 N Vertical component R sin 30 =1276.04 cos 30 = 638.02N

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