The arm of a crane at a construction site is 19.0 m long, and it makes an angle of 14.3° 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 638 N?
Answer in units of N•m.
To find the maximum torque the crane can withstand, we need to multiply the maximum load by the lever arm.
The lever arm is the distance between the point where the force is applied (the load) and the point of rotation (the base of the arm). In this case, the lever arm is the length of the arm of the crane.
Torque (τ) is given by the equation τ = F * r, where F is the force applied and r is the lever arm.
Substituting the given values, we have τ = 638 N * 19.0 m * sin(14.3°).
Using a calculator, we find the maximum torque is approximately 2683 N·m.