Two men are carrying a girl on a large plank that is 10m long and weights 200N. If the girl on a plank weighs 445N and sits 3m from one end, how much weight must each man support?
387N
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To determine how much weight each man must support, we can use the concept of torque. Torque, denoted by τ (tau), is the measure of the force's ability to cause an object to rotate around a pivot point.
We can calculate the torque exerted by the girl on the plank using the formula:
τ = r * F
Where:
τ = torque
r = distance from pivot point (in this case, one end of the plank) to the line of action of the force
F = force exerted by the girl
Given that the girl weighs 445N and sits 3m from one end of the plank, let's calculate the torque exerted by her:
τ = 3m * 445N = 1335 N·m
Since the plank is in equilibrium (not rotating around the pivot point), the torque exerted by the girl must be balanced by the torque exerted by the two men.
Since the plank is symmetrical and we want to find the weight supported by each man, the torque exerted by each man must be equal.
Let's denote the weight supported by each man as W. The distance from the pivot point to each man is 5m (half the length of the plank). Thus, the torque exerted by each man can be calculated using the same formula:
τ = r * F
τ = 5m * W
Since the torque exerted by each man must be equal to the torque exerted by the girl:
5m * W = 1335 N·m
Let's solve for W:
W = 1335 N·m / 5m
W = 267 N
Therefore, each man must support a weight of 267N.