The figure (Figure 1) shows a model of a crane that may be mounted on a truck.A
ID: 1467211 • Letter: T
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 = 85.00 kg and length L = 5.700 m is supported by two vertical massless strings. String A is attached at a distance d = 1.700 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 = 5.500 m from the left end of the bar. Throughout this problem, positive torque is counterclockwise and use 9.807 m/s2 for the magnitude of the acceleration due to gravity.
Find TA, the tension in string A.
Find TB, the magnitude of the tension in string B.
Explanation / Answer
Let TA and TB are tension in the strings.
As the bar is in equilibrium, net force and net torque acting on the bar musy be zero.
Apply net torque about left end = 0
TA*d - m1*g*(L/2) - m2*g*x = 0
TA*d = m1*g*(L/2) + m2*g*x
TA = (m1*g*(L/2) + m2*g*x)/d
= (85*9.8*(5.7/2) + 3500*9.8*5.5)/1.7
= 112367 N <<<<<<<<--------------Answer
Apply Net torue actin about string A = 0
TB*d - m1*g*(L/2 - d) - m2*g*(x - d) = 0
TB*d = m1*g*(L/2 - d) + m2*g*(x - d)
TB = (m1*g*(L/2 - d) + m2*g*(x - d))/d
= (85*9.8*(5.7/2 - 1.7) + 3500*9.8*(5.5 - 1.7))/1.7
= 77234 N <<<<<<<<--------------Answer
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