A seesaw has a mass of 30 kg, a length of 3.0 m, and fulcrum beneath its midpoint. It is balanced when a 50-kg person sits on one end and a 69-kg person sits on the other end.Locate the center of mass of the seesaw (a distance from the 50-kg person).
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To locate the center of mass of the seesaw, we can use the principle of moments.
The principle of moments states that for an object to be in rotational equilibrium, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments.
Let's consider the seesaw balanced on the fulcrum beneath its midpoint. We have two masses acting on the seesaw: the 50-kg person and the 69-kg person.
To find the center of mass, we need to determine the distance from the fulcrum to the center of mass. Let's assume this distance is represented by 'x' meters from the 50-kg person.
The clockwise moments on the seesaw are given by the product of the mass and the distance from the fulcrum. So, the clockwise moment caused by the 50-kg person is (50 * x) N·m.
The counterclockwise moments can be calculated by multiplying the mass with their respective distances from the fulcrum. The counterclockwise moment caused by the 69-kg person is (69 * (3 - x)) N·m.
Since the seesaw is balanced, the sum of the clockwise moments must equal the sum of the counterclockwise moments:
50x = 69(3 - x)
Simplifying this equation, we get:
50x = 207 - 69x
Combining like terms, we have:
119x = 207
Solving for x, we find:
x = 207 / 119
x ≈ 1.74 meters
Therefore, the center of mass of the seesaw is located approximately 1.74 meters from the 50-kg person.