The figure (Figure 1) shows a model of a crane that may be mounted on a truck.A

Question

The figure (Figure 1) shows a model of a crane that may be mounted on a truck.A rigid uniform horizontal bar of mass m1 = 80.0 kg and length L = 5.10 m is supported by two vertical massless strings. String A is attached at a distance d = 1.30 m from the left end of the bar and is connected to the top plate. String B is attached to the left end of the bar and is connected to the floor. An object of mass m2 = 3500 kg is supported by the crane at a distance x = 4.90 m from the left end of the bar. Throughout this problem, positive torque is counterclockwise and use 9.80 m/s2 for the magnitude of the acceleration due to gravity.

Find TA, the tension in string A.

Express your answer in newtons using three significant figures.

Find TB, the magnitude of the tension in string B.

Express your answer in newtons using three significant figures.

Explanation / Answer

mass m1 = 80 kg
L = 5.1 m

String A, tension = Ta, distance from the left end of the bar, d = 1.3 m, connected to top plate
String B, tension = Tb, left end of the bar, connected to te floor
mass m2 = 3500 kg, at distacne d' = 4.9 m from the left end

from force balance
Ta = Tb + (m1 + m2)g

from torque balance about string A
m1g*(L/2 - d) + m2*g*( d' - d) = Tb(d)
[80*(2.55 - 1.3) + 3500(4.9-1.3)]*9.81 = Tb*1.3
Tb = 95836.1538 N
Ta = 130955.95 N

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