A 1400-N uniform boom at ϕ = 70.0° to the horizontal is supported by a cable at an angle θ = 20.0° to the horizontal as shown in the figure below. The boom is pivoted at the bottom, and an object of weight w = 2250 N hangs from its top.
(a) Find the tension in the support cable.
kN
(b) Find the components of the reaction force exerted by the pivot on the boom.
horizontal component
kN right
vertical component
kN upward
i need help starting this problem
Sorry, but there's no figure.
If what I think is happening is happening, then you need to sum the torques around the pivot. The boom and the mass are trying to spin clockwise and the cable is pulling counterclockwise. You'll need some trig to find distances and components.
From that you can get tension. For the reaction forces sum all forces x and y. They all sum to zero.
To start solving this problem, you need to break down the forces acting on the boom and analyze the equilibrium conditions. Here are the steps to get started:
1. Identify the forces: The forces acting on the boom are the tension in the support cable, the weight of the boom itself, and the weight of the hanging object.
2. Draw a free-body diagram: Draw a diagram of the boom and label all the forces acting on it. In this case, draw a horizontal line to represent the boom and show the forces acting on it, such as the tension in the support cable, the weight of the boom, and the weight of the hanging object.
3. Decompose the weight forces: Since the weight forces act at an angle to the horizontal, you need to decompose them into their horizontal and vertical components. To do this, you can use trigonometric functions such as sine and cosine. The weight of the boom can be decomposed into a horizontal component (W_h) and a vertical component (W_v), and the weight of the hanging object can also be decomposed into a horizontal component (w_h) and a vertical component (w_v).
4. Apply the equilibrium conditions: In order for the boom to be in equilibrium, the sum of the forces in both the horizontal and vertical directions must equal zero. Write down the equilibrium conditions by setting up two equations: one for the horizontal forces and one for the vertical forces. These equations will involve the tension in the support cable, the horizontal and vertical components of the weight forces, and the reaction forces at the pivot point.
By following these steps, you'll be on the right track to solve the problem and find the tension in the support cable, as well as the components of the reaction force exerted by the pivot on the boom.