What maximum torque can the crane withstand if the maximum load the crane can handle is 450 N? Answer in units of N · m

Question

The arm of a crane at a construction site is 17.0 m long, and it makes an angle of 14.2 ◦ with the horizontal. Assume that the maximum load the crane can handle is limited by the amount of torque the load produces around the base of the arm. What maximum torque can the crane withstand if the maximum load the crane can handle is 450 N? Answer in units of N · m.

Answer 1

Hi Christina,

The torque (τ) acting on the arm of the crane can be calculated using the formula: τ = r⋅F⋅sin(θ)

where:

1. r is the length of the arm (17.0 m),
2. F is the force applied at the end of the arm (450 N),
3. θ is the angle between the arm and the horizontal (14.2°).

Substitute the given values into the formula: τ=17.0m⋅450N⋅sin(14.2∘) ≈ 1946.25N⋅m

Therefore, the maximum torque the crane can withstand is approximately 1946.25N⋅m.