A 4.10 m long, 590 kg steel beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. A 66.0 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)
To find the magnitude of the torque about the point where the beam is bolted into place, we need to consider the force applied by the construction worker and the lever arm.
The torque is calculated using the formula:
Torque = Force x Lever Arm
1. First, let's calculate the lever arm. The lever arm is the perpendicular distance between the point where the force is applied and the point of rotation (in this case, where the beam is bolted into place).
Given:
Length of the beam (L) = 4.10 m
The construction worker is standing at the far end of the beam, so the distance between the bolted point and the construction worker can be considered as the lever arm:
Lever Arm (r) = Length of the beam (L) = 4.10 m
2. Now, let's calculate the force applied by the construction worker.
Given:
Mass of the construction worker (m) = 66.0 kg
Acceleration due to gravity (g) = 9.8 m/s^2
The weight of the construction worker is given by the formula:
Weight = Mass x Acceleration due to gravity
Weight = m x g
Weight = 66.0 kg x 9.8 m/s^2
Force (F) = Weight = 66.0 kg x 9.8 m/s^2
3. Finally, let's calculate the torque using the formula mentioned earlier.
Torque = Force x Lever Arm
Torque = F x r
Substituting the values calculated earlier:
Torque = F x r
Torque = (66.0 kg x 9.8 m/s^2) x 4.10 m
Now, let's calculate the torque:
Torque = (66.0 kg x 9.8 m/s^2) x 4.10 m
Simplifying the equation:
Torque = 25653.6 N*m
Therefore, the magnitude of the torque about the point where the beam is bolted into place is 25653.6 N*m.