Two people of different weights are standing on opposite ends of a plank that is balanced on a pivot point. If one person weighs 60 kg and the other weighs 80 kg, and the heavier person stands 1 meter from the pivot, how far from the pivot should the lighter person stand for the plank to remain balanced?
Question
Two people of different weights are standing on opposite ends of a plank that is balanced on a pivot point. If one person weighs 60 kg and the other weighs 80 kg, and the heavier person stands 1 meter from the pivot, how far from the pivot should the lighter person stand for the plank to remain balanced?
Solution
To balance the plank, the product of the weight and distance from the pivot point must be the same for both people. This is because the torque (rotational force) on each side of the pivot must be equal for the plank to be balanced.
The torque is calculated by multiplying the weight by the distance from the pivot point. So, for the heavier person, the torque is 80 kg * 1 m = 80 kg*m.
To find out how far the lighter person should stand from the pivot, we set their torque equal to the heavier person's torque and solve for the distance:
60 kg * x m = 80 kg*m
Dividing both sides by 60 kg, we get:
x m = 80 kg*m / 60 kg = 1.33 m
So, the lighter person should stand 1.33 meters from the pivot for the plank to remain balanced.
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