A 4.60-m-long, 580 kg steel beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. A 72.0 kg construction worker stands at the far end of the beam. What is the magnitude of the torque about the point where the beam is bolted into place? In N*m
550*74+4.6*2.3
1723.2 Nm
To find the magnitude of the torque about the point where the beam is bolted into place, we need to understand the concept of torque and how it is calculated.
Torque, represented by the symbol τ (tau), is a measure of the tendency of a force to cause rotation about an axis or point. It is calculated by multiplying the force applied by the perpendicular distance (lever arm) between the point of rotation and the line of action of the force.
In this case, the construction worker standing at the far end of the beam exerts a downward force due to their weight. The torque can be calculated as follows:
Torque = Force × Lever Arm
The force is equal to the weight of the construction worker, which can be calculated as follows:
Force = mass × acceleration due to gravity
Given:
Mass of the beam (m1) = 580 kg
Length of the beam (L) = 4.60 m
Mass of the construction worker (m2) = 72.0 kg
To find the magnitude of the torque, we need to determine the lever arm. In this case, the lever arm is the perpendicular distance between the point of rotation (where the beam is bolted) and the line of action of the force (the end of the beam where the construction worker is standing).
The lever arm can be calculated as:
Lever Arm = Length of the beam + Half the width of the construction worker
Assuming the width of the construction worker is negligible compared to the length of the beam, we can use the length of the beam as the lever arm.
Now, let's calculate the torque:
Force = m2 × g
= 72.0 kg × 9.8 m/s² [using the acceleration due to gravity, g ≈ 9.8 m/s²]
Torque = Force × Lever Arm
= (72.0 kg × 9.8 m/s²) × 4.60 m
Calculating this, we find:
Torque ≈ 3,151.68 N*m
Therefore, the magnitude of the torque about the point where the beam is bolted into place is approximately 3,151.68 N*m.