Timer Notes Evaluate Feedback Print Info 18-7,8 Due in 6 Horizontal hours, 16 mi
ID: 3164122 • Letter: T
Question
Timer Notes Evaluate Feedback Print Info 18-7,8 Due in 6 Horizontal hours, 16 minutes Beam plus Load A uniform, 12.5 kg beam of length 3.10 m is hanging horizontally as shown in the diagram below. It is pinned to a vertical wall at point B and supported by a thin, massless wire connected at point Con the beam and at point A on the wall. IUse g -980 m/s There is a load W, with a weight of 198 N, hanging at the end of the beam. The distance AB is 2.64 m, and the distance BC is 2.11 m. The distance BD is 3.10 m. What is the tension in the wire? Submit Answer Tries 0/15 Find the horizontal and vertical components of the force on the horizontal beam at the joint B. Use for forces up or to the right, for forces down or to the left Submit Answer Tries 0/15Explanation / Answer
According to the given problem,
To determine the angle between the wire and horizontal, I used the following equation.
Tan = AB ÷ BC
Tan = 2.64 ÷ 2.11
The angle is approximately 51.4
AC is the length of the wire.
AC = (2.642 + 2.112) = 3.38
This is approximately 3.38 meters.
Weight of beam = 12.5 * 9.8= 122.5 N
This is at the center of the beam.
This is a torque problem. Let the pivot point be at point B. The weights of beam and load will produce clockwise torque. The vertical component of the tension in the wire produces counter clockwise torque.
Clockwise torque = 122.5 * 1.55 + 198 * 3.10 = 803.675
Vertical component = T * 2.64 ÷ 3.38
Distance = 2.11 meters
Counter clockwise torque = T * 2.64 ÷ 3.38 * 2.36 = T *1.84
T * 1.84 = 803.675
T = 436 N
The tension is approximately 436 N. Let’s determine the vertical and horizontal component of the tension.
Vertical component = 436 * (2.64 ÷3.38)
This is approximately 340.54 N
Total weight = 122.5 + 198 = 320.5 N
Vertical force at the hinge = 340.54 – 320.5
This is approximately 20.04 N upward.
The horizontal force at the hinge B is equal in magnitude to the horizontal component of the tension.
Horizontal component = 436 * (2.11 ÷ 3.38)
Horizontal component = 272.177 N
This is approximately 272.177 N.
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