Answer to Question #117791 in Mechanics | Relativity for PK

Question

A 12.2 m crane weighs 18.0 kN and is lifting a 50.4 kN load. The hoisting cable (tension T1) passes over a pulley at the top of the crane and attaches to an electric winch in the cab. The pendant cable (tension T2) which supports the crane, is fixed to the top of the crane.

a) Find the tensions in the two cables.

When the crane in question above is in the position shown and lifts a 70.8 kN load, the tension T2 = 260 kN. For this situation;

b) Determine the magnitude of the force exerted by the pivot P to maintain static equilibrium.

c) At what angle to the horizontal x-axis is this force FP acting?

Answer 1

a)

Apply lami's Therom

$\frac{50.4}{sin45}= \frac{T_{1}}{sin45} =\frac{T_{2}}{sin45}$

$T_{1} = 50.4 kN$

$T_{2} = -71.27kN$

b)

apply equilibrium condition,

$\Sigma F_{y} =0$

$p_{y} = 71.8 +260 sin45 = 255.64 kN$

$p_{x} = 260 cos45 +71.27=255.12 kN$

$p = \sqrt{p_{x}^{2}+p_{y}^{2}} = 361.18 kN$

angle of force P

$\theta = tan^{-1}(\frac{255.64}{255.12})= 45.06 ^{0}$