Question

Determine the largest weight w that can be supported by the boom?

Answer 1

The largest weight w that can be supported by the boom is determined by the equilibrium of torques, and it is given by the formula
`\(w = (F * d)/(\sin(\theta))\)`, where F is the force applied, d is the lever arm distance, and
`\(\theta\)` is the angle of the boom.

Step-by-step explanation:

To find the largest weight w that the boom can support, we use the equilibrium condition for torques. The torque
`(\(\tau\))` is the product of the force F and the lever arm distance d, given by the formula
`\(\tau = F * d * \sin(\theta)\)`. In equilibrium, the sum of torques acting on the system is zero. Therefore, setting
`\(\tau\)` to zero, we get
`\(F * d * \sin(\theta) = 0\).`

However, we are interested in the largest weight \(w\) that the boom can support, meaning the forceF is directed vertically downward. In this case, the sine of the angle
`(\(\theta\)`) becomes 1. Therefore, the formula for the largest weight w is
`\(w = (F * d)/(\sin(\theta))\)`becomes
`\(w = F * d\).` This is because
`\(\sin(\theta)\)`is equal to 1 when the force is acting vertically downward.

Calculating w involves knowing the applied force F and the lever arm distance d. By substituting these values into the formula, we can find the maximum weight that the boom can support while maintaining equilibrium. Understanding torque and its relationship with force, distance, and angle is crucial for determining weight limits in scenarios involving lever systems, such as the described boom.