A 4-m-long I-beam (of uniform shape) having a mass of 48 kg is held at a 35º angle above the floor by a bracket attached to its end. The bracket is securely bolted to the floor. The torque that the bracket must provide to hold the I-beam in place is
A) 540 Nm.
B) 770 Nm.
C) 610 Nm.
D) 660 Nm.

Question

Quizplus · Accepted Answer

The torque ($ \tau $) required to hold the I-beam in place can be calculated using the formula $ \tau = rF\sin(\theta) $, where $ r $ is the distance from the pivot point to the point of force application, $ F $ is the force (in this case, the weight of the I-beam), and $ \theta $ is the angle between the force direction and the lever arm. The weight of the I-beam is $ F = mg = 48 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 470.4 \, \text{N} $. The distance $ r $ is half the length of the I-beam since its mass is uniformly distributed, so $ r = 2 \, \text{m} $. Therefore, $ \tau = 2 \times 470.4 \times \sin(35^\circ) \approx 770 \, \text{Nm} $.

A 4-M-Long I-Beam (Of Uniform Shape) Having a Mass of 48