Question

The beam ABC has a mass of 78.0 kg and is supported by the rope BDC that runs through the frictionless pulley at D. The winch at CC has a mass of 44.5 kg. The tension in the rope acts on the beam at points B and C and counteracts the moments due to the beam's weight (acting vertically at the midpoint of its length) and the weight of the winch (acting vertically at point C) such that the resultant moment about point A is equal to zero. Assume that rope segment CD is vertical and note that rope segment BD is not necessarily perpendicular to the beam.

a.) Compute the tension in the rope.

b.) Model the two forces the rope exerts on the beam as a single equivalent force and couple moment acting at point B. Enter your answer in Cartesian components.

c.) Model the two forces the rope exerts on the beam as a single equivalent force (no couple) and determine the distance from A to the point along the beam where the equivalent force acts (measured parallel to the beam from A). Enter your answer in Cartesian components.

frietionless ulle 8 winch BY NC SA 2013 Michael Swanbom

Values for dimensions on the figure are given in the following table. Note the figure may not be to scale.

Variable Value

a 2.55 m

b 3.19 m

c 1.66 m

d 4.88 m

a.) The tension in the rope is ______N.

b.) The equivalent force and couple system acting at B consists of a force →Feq = ( ___ˆi + ____ˆj) N,
and a couple →Meq = _____ˆk N-m.

c.) The tension forces can also be modeled by an equivalent force of →Feq = ( ____ˆi + ____ˆj) N
acting at a point _____ meters along the beam from A.

Answer 1

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at& no 2) 1813 97 + 20科,352 (o(S, u S x χν Sin 2-9q