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If a person weighing 60 kg sits on one end of a teeter-totter, the distance between the person and the fulcrum is 3 meters. How much weight is needed on the other end to balance the teeter-totter if the distance between the weight and the fulcrum is 4 meters?
Detailed Explanation
To balance the teeter-totter, the torques on both ends of the fulcrum need to be equal. Torque is calculated by multiplying the weight by the distance from the fulcrum.
Let's assume the weight needed on the other end to balance the teeter-totter is W (in kilograms).
The torque exerted by the person sitting on one end is calculated as follows:
Torque of person = Weight of person × Distance of person from fulcrum
= 60 kg × 3 meters
= 180 kg·m
To balance the teeter-totter, the torque exerted by the weight on the other end must be equal:
Torque of weight = Weight of weight × Distance of weight from fulcrum
Since the torques on both ends need to be equal, we can set up the equation:
Torque of person = Torque of weight
180 kg·m = Weight of weight × 4 meters
Now, we need to solve for the weight of weight (W):
Weight of weight = 180 kg·m / 4 meters
Weight of weight = 45 kg
Therefore, to balance the teeter-totter, a weight of 45 kg is needed on the other end, considering the different distances between the person and the fulcrum (3 meters) compared to the weight and the fulcrum (4 meters).
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