Question

The jib crane shown is oriented so that its boom ad is parallel to the x axis and is used to move a heavy crate. Knowing that the tension in cable ab is 2.6 kips, replace the force exerted by the cable at a by an equivalent force-couple system at the center o of the base of the crane. What is the equivalent force exerted by the cable at a?

1) 2.6 kips
2) Cannot be determined
3) Depends on the weight of the crate
4) None of the above

Answer 1

The equivalent force exerted by the cable at point A is 2.6 kips, which is simply the tension in the cable. The moment at the base center O cannot be determined without the perpendicular distance from O to the force's line of action.

Step-by-step explanation:

To replace the force exerted by the cable at A by an equivalent force-couple system at the center O of the base of the crane, we need to find the force exerted along the cable at point A and the moment created by this force about the center O. Since the tension in the cable AB is given as 2.6 kips and the cable is assumed to be perfectly flexible (meaning there is no force required to bend the cable and tension is equal along the cable), the force exerted by the cable at A is indeed 2.6 kips. The fact that the boom is parallel to the x-axis makes this force horizontal at A. The moment (torque) at O due to this force depends on the perpendicular distance from O to the line of action of the force, which is not given in the question. Therefore, the equivalent force exerted by the cable at A is simply the tension in the cable, which is 2.6 kips, and the question does not provide enough information to determine the moment (or the couple) at O without this distance.