Three men 4, apart are carrying a heavy load on a pole. Two are one end of the pole and the third is at the other end. Where should the load be placed so that each man gives equal support?
what does three men 4 mean?
oh sorry, 4 meters apart, I mean.
Pick an end and sum moments:
I will start at the two men end.
W*L-F*4=0
Now if each is "shouldering" and equal weight, then F=W/3
put that in the equation and solve for L, the length for the weight from the two men end.
oh, ok, I see; i had thouht of something along those lines, but was thrown off by seeing two variables, but now I see how that can be done; thank you!
To find the position where the load should be placed for each man to give equal support, we need to consider the principle of moments or torques. The principle of moments states that the sum of the moments acting on an object must be zero for it to be in rotational equilibrium.
In this case, each man exerting a force on the pole can be considered as a separate force acting at a specific distance from a reference point. Let's assume that the two men at one end of the pole are referred to as A and B, and the man at the other end is C.
To have equal support from each man, the total moment exerted by A and B must be equal to the moment exerted by C. Mathematically, we can express this as:
(A's force) x (distance of A from the load) + (B's force) x (distance of B from the load) = (C's force) x (distance of C from the load)
Since we are assuming that the distances between the men are equal (4 units apart), we can simplify the equation to:
(A's force) x (4) + (B's force) x (4) = (C's force) x (4)
Since we don't have any specific values for the forces exerted by the men, we can consider them as F1, F2, and F3, and rewrite the equation as:
(4F1) + (4F2) = (4F3)
We can then simplify further to:
4F1 + 4F2 = 4F3
Now, in order for the equation to hold true, it means that the sum of the forces exerted by A and B must be equal to the force exerted by C.
Therefore, the load should be placed at the midpoint between the two men on one end of the pole (A and B), so that each man will be 2 units away from the load. This will ensure that the distance from the load to A is equal to the distance from the load to B. By placing the load at this position, A and B will exert equal forces, resulting in each man giving equal support.