Question

A 15,000 N crane pivots around a friction-free axle at its base and is supported by a cable making a 25∘ angle with the crane (Figure 1). The crane is 16 m long and is not uniform, its center of gravity being 7.0 m from the axle as measured along the crane. The cable is attached 3.0 m from the upper end of the crane.

When the crane is raised to 55∘ above the horizontal holding an 11,000 N pallet of bricks by a 2.2 m very light cord, find the tension in the cable.

Find the horizontal component of the force that the axle exerts on the crane

Find the vertical component of the force that the axle exerts on the crane.

2.2-m cord Bricks Cable 55° Axle 250 25o 3.0 m-

Answer 1

Ansuner 3m Grunnen that W, = 15000N, 0, -25°, 1=16m center of granity of crame 7cm foumoale cable is attached 3 m from upper endg crane 0:55", Wb=11000N, d=212m FBD: TCOD30) N a 13" T30 V11000N Mam do sovom" TsinBoy A EX we know that {TAGO TX13Sun(25) - I love x16 sin(354) --15000 X7 Sun 35= 0 T- 100949,45+ 60225.526 13x Sun25) T=29336.345 N T= 2,93x109N

{ Fry To Fy -15000 - 11000 -T Sun(30°) = 0 F = 15000+ 11000+2.93xlox.sinBoy) = Fy= 40668,192 N EFxzo Fe - TCORBU) = 0 Fx = 2.93x10°x20330) Fx=25344.54N Fx=2,5310 N