A 5.00-meter steel beam of uniform cross section and composition weighs 100 N. What is the minimum force required to lift one end of the beam?
To determine the minimum force required to lift one end of the steel beam, we need to consider the weight of the beam and the distance from the pivot point (fulcrum) to the beam's center of mass.
Given:
- Length of the steel beam, L = 5.00 meters
- Weight of the beam, W = 100 N
We can start by calculating the location of the beam's center of mass. Since the beam has a uniform cross section and composition, the center of mass will be at the midpoint of the beam.
Center of mass distance, d = L/2 = 5.00 meters / 2 = 2.50 meters
Next, we can calculate the torque exerted by the weight of the beam about the pivot point. Torque is given by the formula:
Torque = Force × Distance
The torque exerted by the weight of the beam can be expressed as:
Torque = Weight × Distance = W × d
Substituting the given values:
Torque = 100 N × 2.50 meters = 250 N·m
Finally, the minimum force required to lift one end of the beam is equal to the torque exerted by the weight. Therefore, the minimum force required is 250 N.