The figure (Figure 1) shows a model of a crane that may be mounted on a truck.A
ID: 1485774 • 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 = 75.00 kg and length L = 5.100 mis supported by two vertical massless strings. String A is attached at a distance d = 2.000 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 = 2000kg is supported by the crane at a distance x = 4.900 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.
1.)Find
TA, the tension in string A.
2.)Find TB, the magnitude of the tension in string B.
Explanation / Answer
if the system is in equilibrium, rthe net torque is zero.
TAd - m1g[L/2] -m2gx = 0
rewrite the equation for TA.
TA = m1g[L/2] + m2gx
= {75*9.8[5.1/2] + 2000*9.8*4.9}/d
= 48957.125 N
if the system is in equilibrium, rthe net torque is zero.
TBd - m1g[0.5L-d] -m2g(x-d) = 0
rewrite the equation for TB.
TB = {m1g[0.5L-d]+m2g(x-d)}/d
= {75*9.8*[0.5*5.1-2]+2000*9.8*(4.9-2)}/2
= 28622.125 N
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