Question

A 4.0-m-long, 500 kg steel beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. A 70 kg construction worker stands at the far end of the beam. What is the magnitude of the torque about the bolt due to the worker and the weight of the beam?

Accepted Answer

Step 1: Understand the concept of torque. Torque is the rotational equivalent of force and is calculated using the formula: τ=r⋅F⋅sin(θ), where r is the distance from the pivot point, F is the force applied, and θ is the angle between the force and the lever arm. In this problem, the angle is 90 degrees, so sin(90)=1. Step 2: Calculate the torque due to the construction worker. The force exerted by the worker is his weight, which is given by F=m⋅g, where m is the mass of the worker (70 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²). The distance r is the length of the beam (4.0 m). Use the formula for torque: τ=r⋅F. Step 3: Calculate the torque due to the weight of the beam. The beam's weight acts at its center of gravity, which is located at the midpoint of the beam (2.0 m from the bolt). The force exerted by the beam is its weight, given by F=m⋅g, where m is the mass of the beam (500 kg) and g is the acceleration due to gravity (9.8 m/s²). Use the formula for torque: τ=r⋅F. Step 4: Add the torques together. Since both the worker and the beam exert forces that cause rotation in the same direction about the bolt, their torques can be added directly. The total torque is the sum of the torque due to the worker and the torque due to the beam. Step 5: Ensure units are consistent. Verify that all distances are in meters, masses are in kilograms, and forces are in newtons. This ensures the torque is calculated in newton-meters (N·m).

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Torque

Center of Mass

Equilibrium