A uniform beam of length L = 8.00 m and weight 3.80 102 N is carried by two workers, Sam and Joe, as shown in the figure below. Determine the force that each person exerts on the beam.
To determine the force that each person exerts on the beam, we need to consider the torque balance.
Torque is the product of the force and the perpendicular distance from the point of rotation. In this case, the point of rotation is the center of the beam.
Let's assume that Sam is closer to the left end of the beam, and Joe is closer to the right end of the beam. The distances from the point of rotation to Sam and Joe are d1 and d2 respectively.
First, we can calculate the weight of the beam. The weight is given as 3.80 * 10^2 N.
Next, we need to find the torque exerted by the weight of the beam. The torque exerted by the weight of the beam at the center of the beam is zero since the perpendicular distance is zero.
Now, we can set up the torque balance equation:
Torque exerted by Sam - Torque exerted by Joe = 0
The torque exerted by Sam can be calculated as the product of the force exerted by Sam and the perpendicular distance from the point of rotation to Sam (d1). Similarly, the torque exerted by Joe can be calculated as the product of the force exerted by Joe and the perpendicular distance from the point of rotation to Joe (d2).
Since the beam is uniform and in equilibrium, the torques exerted by Sam and Joe must be equal.
Therefore, we have:
Force exerted by Sam * d1 = Force exerted by Joe * d2
We can rearrange this equation to solve for the force exerted by Sam:
Force exerted by Sam = (Force exerted by Joe * d2) / d1
Substituting the given values:
Force exerted by Sam = (Weight of the beam * d2) / d1
Finally, we can substitute the given values for d1 and d2, which are the distances from the center of the beam to Sam and Joe respectively.
After substituting the values, we can calculate the force exerted by Sam and Joe using the calculated formula.