when one boy is sitting 1.20 meter from the center of he seesaw the girl must sit on the other side 1.50 meter from the center to maintain an even balance . however the boy carries an additional mass pf 14 kg and sit 1.80 meter from the center the girl must move to 3 meter from the center to balance . neglecting the weight of the seesaw find the weight of the boy and the girl?
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To solve this problem, we can apply the principle of moments. The principle of moments states that in order 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 denote the weight of the boy as Wb, the weight of the girl as Wg, the distance of the boy from the center as db, the distance of the girl from the center as dg.
In the first scenario, when the boy is sitting 1.20 meters from the center and the girl is sitting 1.50 meters from the center, the principle of moments can be written as:
(Wb * db) = (Wg * dg)
In the second scenario, when the boy is sitting 1.80 meters from the center and the girl moves to 3 meters from the center, the principle of moments can be written as:
(Wb * db) = (Wg * dg)
Notice that the distances for the boy and girl are different in the two scenarios. We can solve these equations simultaneously to find the weights of the boy and girl.
From the first equation:
Wg = (Wb * db) / dg
Substituting this value into the second equation:
Wb * db = ((Wb * db) / dg) * 3
Simplifying:
Wb * db = (Wb * db * 3) / dg
Canceling out the common terms:
1 / dg = 3
Simplifying:
dg = 1 / 3
Now we can substitute this value of dg back into the first equation to solve for Wg:
Wg = (Wb * db) / (1/3)
Simplifying:
Wg = (Wb * db) * 3
From the information given, we know that the boy carries an additional mass of 14 kg. So, we can denote the weight of the boy as Wb = 14g, where g is the acceleration due to gravity (9.8 m/s^2).
Now we can substitute the known values into the equation for Wg to solve for Wg:
Wg = (14g * db) * 3
From the given information, we know that db = 1.80 meters. Substituting this value:
Wg = (14 * 9.8 * 1.80) * 3
Simplifying:
Wg = 75.24 kg
Therefore, the weight of the girl is approximately 75.24 kg. To find the weight of the boy, we can substitute this value back into the equation Wg = (Wb * db) * 3:
75.24 = (14 * 9.8 * 1.80) * 3
Simplifying:
Wb = 73.88 kg
Therefore, the weight of the boy is approximately 73.88 kg.