Question

A Bar Suspended by Two Vertical Strings

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 = 80.00kg and length L = 5.100m is supported by two vertical massless strings. String A is attached at a distance d = 1.200m 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 = 3500kg is supported by the crane at a distance x = 4.900m from the left end of the bar.

Throughout this problem, positive torque is counterclockwise and use 9.807m/s2 for the magnitude of the acceleration due to gravity.

Find TA, the tension in string A. Express your answer in newtons using four significant figures.

Find TB, the magnitude of the tension in string B. Express your answer in newtons using four significant figures.

Answer 1

To find the tension in string A, divide the torque due to the weight of the bar by the distance from string A to the center of mass of the bar and the load. To find the tension in string B, subtract the weight of the bar and the load from the total vertical force.

Step-by-step explanation:

To find the tension in string A, we can analyze the torque acting on the bar about the point where string A is attached. The torque due to the weight of the bar (m1g) will be balanced by the torque due to the tension in string A (TA). The torque about the pivot point will be equal to m1g * d, where d is the distance from the pivot point to string A. Therefore, we can calculate TA by dividing m1g * d by the distance x from string A to the center of mass of the bar and the load:

TA = (m1 * g * d) / x

To find the tension in string B, we can analyze the vertical forces acting on the bar. The weight of the bar (m1g), the weight of the load (m2g), and the tension in string A (TA) will add up to the total vertical force (m1g + m2g). Therefore, we can calculate TB by subtracting the weight of the bar and the load from the total vertical force:

TB = (m1 + m2) * g - m1 * g