The figure shows a model of a crane that may be mounted on a truck.A rigid unifo

Question

The figure shows a model of a crane that may be mounted on a truck.A rigid uniform horizontal bar of mass m_1 = 85.00 kg and length L = 5.700 m is supported by two vertical massless strings. String A is attached at a distance d = 1.600 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 m_2 = 2000 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/s^2 for the magnitude of the acceleration due to gravity.

A. Find T_A, the tension in string A.

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

Explanation / Answer

A) Setting the pivot point at B, we must set up all of theforces in equilibrium.
Notice that the center of gravity of the rod is at L/2.
Counterclockwise is negative, clockwise is positive.

So,
-TA*d + m1*g*L/2 + m2*g*x = 0
(m1*L/2 + m2*x)*g = TA*d
TA = (m1*L/2 + m2*x)*g/d
TA = (85*2.85 + 2000*5.5)*9.807/1.6
TA = 68907.96609 N


B)
Same as before, only now with A as the pivot point.

-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
TB = 48460.37109 N

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