The bar of a crane begins at a point r_1 vector = (0) I cap + (- 20.0 ft) j cap

Question

The bar of a crane begins at a point r_1 vector = (0) I cap + (- 20.0 ft) j cap + (0.00 ft) k cap, and ends at the point r_2 vector = (0)I cap + (0.00 ft)j cap + (30.0 ft)k.A cable carrying a tension of 280 lbs stretches from the end (r_2 vector) of the crane to a point r_3 vector = (12.0 ft)I cap + (10.0 ft)j cap + (0.00 ft)k cap. What is a unit vector in the direction of the tension? What is the tension in the cable, in component form? What is the moment of the cable about the base of the crane?

Explanation / Answer

a. tension is in the direction of r3-r2

r3 - r2 = (12-0)i + (10-0)j+(0-30)k

r3 - r2 = 12i+10j-30k

Unit vector = (12i+10j-30k)/ (122 + 102 + (-30)2)

Unit vector = 0.355i + 0.296j - 0.887

b. Tension = 280*(0.355i + 0.296j - 0.887)

Tension = 99.4i + 82.88j - 248.36k lbs

c. r2-r1 = 20j+30k

Moment = (r2-r1)×T

M = (20j+30k) × (99.4i + 82.88j - 248.36k) where × is cross product

M = -7453.6i +2982j -1988k lbs.ft

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