A rigid uniform horizontal plank of mass m1 = 91 kg and length L = 7.9 m is supp

Question

A rigid uniform horizontal plank of mass m1 = 91 kg and length L = 7.9 m is supported by two vertical strings as shown above.
String A is attached at a distance of d = 1.6 m from the left end of the bar and is connected to the ceiling.
String B is attached to the left end of the bar and is connected to the floor.
An object of mass m2 = 1610 kg is supported by the crane at a distance x = 6.1 m from the left end of the bar.

Calculate the tension in string A.

Calculate the tension in string B.

Calculate the mass m needed in order to suspend the leg shown in figure below.

Assume the leg (with cast) has a mass of 14.2 kg, and its CG is 34.2 cm from the hip joint; the sling is 72.0 cm from the hip joint.

Explanation / Answer

1) T1*d = m2*g*x + m1*g*L/2

=>T1 = (1610*9.8*6.1 + 91*9.8*7.9/2)/1.6 = 62355.26 N

T2*d = m2*g*(x-d) + m1*g*(L/2-d)

=> T2 = (1610*9.8*(6.1-1.6) + 91*9.8*(7.9/2-1.6))/1.6 = 45685.46 N

2) m*g*72 = M*g*34.2

=>m = 14.2*34.2/72 = 6.745 kg

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