Problem 10.42 The boom in the figure below (Figure 1) weighs 3000 N and is attac

Question

Problem 10.42 The boom in the figure below (Figure 1) weighs 3000 N and is attached to a frictionless pivot at its lower end. It is not uniform; the distance of its center of gravity from the pivot is 32 % of its length. Find the tension in the guy wire. Express your answer in newtons to three significant figures. Find the horizontal component of the force exerted on the boom at its lower end. Express your answer in newtons to three significant figures. Find the vertical component of the force exerted on the boom at its lower end. Express your answer in newtons to three significant figures.

Explanation / Answer

From the given figure

In the vertical direction

The weight of the boom =3000N in the downward direction

The weight of the mass attached at the boom is =5000N in the downward direction

The total vertical force on the boom's pivot at the wall is =8000N

now in the horizontal direction

Tension in the guy wire =Tension ot the left

Therefore the horizontal force on the boom's pivot at the wall =Tension newtons to the right

We can consider the torque a the piovt =Zero

Now if consider the toruqe in clockwise direction =counterclockwise torque

Tsin60*L =(3000)(sin30)(0.320L)+(5000N)sin30)(L)

T =(480L+2500L)/L*sin60 =2980L/0.866L=3441N

Now the force acting on the boom at its pivot is

Fx =T =3441N to the right

and Fy = 8000N in the upward direction

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