Assume concurrent forces. Show all the steps. Box your answers. Include proper u

Question

Assume concurrent forces. Show all the steps. Box your answers. Include proper units in your answer. BE NEAT Problem 2 Rods AC and BC are attached to the vertical wall (AB), as shown, with smooth rings at A, B and C. The structure supports a horizontal load of magnitude 400 lbs. The distance between points A and B is 14 feet. The lengths of rods BC and CA are 13 feet and 15 feet, respectively. Neglect the size of the rings. Assuming the horizontal direction to be the x-direction and the vertical direction to be the y-direction: Determine the unit vectors along CA and CB in the Cartesian co-ordinate system.

Explanation / Answer

>> Now, from figure:

Taking B as Origin

=> B = (0,0,0)

=> A = (0,14,0)   [ because, AB = 14 ft]

Now, Let C = (x,y,0)

>> Now, as length of BC = 13 feet

=> [x2 + y2]1/2 = 13

=> [x2 + y2] = 169         ....(1).......

>> Now, as length of CA = 15 feet

=> [x2 + (14 - y)2]1/2 = 15

=> [x2 + (14 - y)2] = 225         ....(2).......

Solving (1) and (2),

=> x = 12 ft

and, y = 5 ft

=> Point C = (12,5,0)

>> Now, Vector CA, CA = (0 i + 14 j + 0 k) - (12 i + 5 j + 0 k)

=> CA = - 12 i + 9 j

Magntude = [122 + 92]1/2 = 15

=> Unit Vector Along CA = (- 12 i + 9 j)/15 = - 0.8 i + 0.6 j

>> Now, Vector CB, CB = (0 i + 0 j + 0 k) - (12 i + 5 j + 0 k)

=> CB = - 12 i + 5 j

Magntude = [122 + 52]1/2 = 13

=> Unit Vector Along CB = (- 12 i - 5 j)/13 = - 0.923 i - 0.385 j

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