A uniform beam of length 7.60 m and weight 3.90 102 N is carried by two workers, Sam and Joe,
Sam=1.00m
Joe=2.00m
between both Joe and Sam there is 7.60m
(a) Determine the forces that each person exerts on the beam.
F_Sam = N
F_Joe = N
(b) Qualitatively, how would the answers change if Sam moved closer to the midpoint?
(c) What would happen if Sam moved beyond the midpoint?
It is not clear from your question what the two distance measurements mean.
Since Sam and Joe are 7.6 m apart, they must be at the ends of the beam
In any case, the problem can be solved by setting the total moment about any point equal to zero. The weight of the beam can be considered to be applied at the middle.
To determine the forces that Sam and Joe exert on the beam, we can use the principle of moments. This principle states that for a body in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the counterclockwise moments about the same point. In this case, we can take the midpoint of the beam as the point of reference.
(a) To find the forces exerted by Sam and Joe, we can start by calculating the total weight of the beam:
Weight = 3.90 * 10^2 N.
Now, let's consider the moments around the midpoint. The moment exerted by Sam (F_Sam) can be calculated by multiplying the weight of the beam by its distance from the midpoint:
Moment_Sam = F_Sam * (7.60/2 - 1.00).
Similarly, the moment exerted by Joe (F_Joe) can be calculated as:
Moment_Joe = F_Joe * (7.60/2 - 2.00).
Since the beam is in equilibrium, the sum of the moments exerted by Sam and Joe must be equal to the weight of the beam:
Moment_Sam + Moment_Joe = Weight.
We can substitute the moments with the force equations and solve for F_Sam and F_Joe:
F_Sam * (7.60/2 - 1.00) + F_Joe * (7.60/2 - 2.00) = 3.90 * 10^2.
Now, with the given distances for Sam (1.00 m) and Joe (2.00 m), we can substitute them into the equation:
F_Sam * (7.60/2 - 1.00) + F_Joe * (7.60/2 - 2.00) = 3.90 * 10^2.
Simplifying the equation will give us the values of F_Sam and F_Joe.
(b) If Sam moves closer to the midpoint, for example, to 0.50 m from the midpoint, the distance between Sam and Joe would decrease. As a result, the moment exerted by Sam would decrease, and the moment exerted by Joe would increase to maintain equilibrium. Therefore, both the forces exerted by Sam and Joe would change.
(c) If Sam moved beyond the midpoint, for example, to 8.00 m from the reference point, the moment exerted by Sam would become negative. In this case, Sam's force would create a clockwise moment, opposite to the counterclockwise moment created by Joe's force. The beam would no longer be in equilibrium, and it would rotate in the direction of the larger moment, causing instability.