Carrying a Uniform Beam: Calculating Joe's Exerted Force

What force does Joe exert on the beam?

A uniform beam of length 7.60 m and weight 450 N is carried by two workers, Sam and Joe. Sam is carrying it at a distance of 1.00 m from one end, while Joe is carrying it at a distance of 2.00 m from the same end. Determine the force that Joe exerts on the beam.

Answer:

The negative sign indicates that Joe is exerting the force in the opposite direction. Therefore, the force that Joe exerts on the beam is 225 N.

To determine the force that Joe exerts on the beam, we need to consider the weight distribution. The beam is 7.60 m long, and we are given that Sam is carrying it at a distance of 1.00 m from one end, while Joe is carrying it at a distance of 2.00 m from the same end.

Since the beam is uniform, its weight is distributed evenly along its length. We can assume that the weight acts at the center of the beam.

To find the force that Joe exerts, we can use the principle of moments. The moment of force exerted by Sam can be calculated by multiplying his force (equal to the weight of the beam) by his distance from the end of the beam. Similarly, the moment of force exerted by Joe can be calculated by multiplying his force (unknown) by his distance from the end of the beam.

Since the beam is in equilibrium, the sum of the moments of the forces exerted by Sam and Joe must be zero. This can be expressed as:

(Moment of force exerted by Sam) + (Moment of force exerted by Joe) = 0

Using the given distances and the weight of the beam, we can set up the equation:

(450 N) * (1.00 m) + (Force exerted by Joe) * (2.00 m) = 0

Simplifying the equation, we get:

450 N + 2 * (Force exerted by Joe) = 0

Rearranging the equation to solve for the force exerted by Joe:

2 * (Force exerted by Joe) = -450 N

Dividing both sides by 2, we find:

The force exerted by Joe = -225 N