of 20 Map apling Learning After an unfortunate accident at a local warehouse you
ID: 777981 • Letter: O
Question
of 20 Map apling Learning After an unfortunate accident at a local warehouse you have been contracted to determine the cause. A jib crane collapsed and injured a worker. An image of this type of crane is shown in the figure below The horizontal steel beam had a mass of 97.00 kg per meter of length and the tension in the cable was 12.43 kN. The crane was rated for a maximum load of 1 000 × 103 lbs. If d-5 870 m, s-0.558 m, x 1.100 m and h 1.890 m, what was the load on the crane before the collapse? What was the magnitude of force at the attachment point P? The acceleration due to gravity is g 9.810 m/s Number Number O Puvcs Check Answer Next Ext HintExplanation / Answer
Sum the moments about the hinge:
0 = T(d - s)sin? - W(d - x) - F(d/2)
where F is the weight of the beam.
? = arctan(h/(d-s)) = arctan(1.890 / 5.312) = 19.58º
so
0 = 12430N*5.312m*sin19.58º - W*4.77m - 97 kg/m*5.870m*9.8m/s²*5.870m/2
4.77W = 5750 N
W = 1205 N ? load
(b) sum the vertical forces:
Fv + Tsin? - W - 97kg/m*5.870m*9.8m/s² = 0
Fv + 12430N*sin19.58 - 1205N - 5580N = 0
Fv = 2619 N ? vertical force at hinge
sum the horizontal forces:
Fh - Tcos? = 0
Fh - 12430N*cos19.58º = 0
Fh = 11711 N ? horizontal force at hinge
mag P = ?(11711² + 2619²) N = 12000.5 N ? total reaction at hinge
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.