When a boy is sitting 1 meter from the center of a see-saw, another boy must sit on the
opposite side 0.5 meter farther from the center compared to the first boy to maintain balance.
When the first boy carries an additional weight of 10 kg and sits 1.5 meters from the center, the
second boy must now move to 3 meters from the center to maintain balance. What is the weight
of the heavier boy?
To figure out the weight of the heavier boy, we can use the principle of moments or torque. The principle of moments states that the total clockwise moment is equal to the total anticlockwise moment when an object is in equilibrium.
Let's break down the problem step by step:
1. Initially, when the first boy is sitting 1 meter from the center, the second boy must sit 0.5 meters farther from the center to maintain balance. This means the second boy is sitting at 1 + 0.5 = 1.5 meters from the center.
2. To calculate the moment (torque), we multiply the weight of each boy by their respective distances from the center. Let's denote the weight of the first boy as W1 and the weight of the second boy as W2.
For the initial scenario, the moment for the first boy is W1 * 1 meter and for the second boy is W2 * 1.5 meters. Since they are in equilibrium, the moments are equal. Mathematically, it can be expressed as:
W1 * 1 = W2 * 1.5
3. Now, the first boy carries an additional weight of 10 kg and sits 1.5 meters from the center. To maintain balance, the second boy must move to 3 meters from the center. The new equation based on the principle of moments is:
(W1 + 10 kg) * 1.5 = W2 * 3
4. To solve this system of equations, we can substitute the value of W2 from the first equation into the second equation:
W1 * 1 = (W1 * 1.5) / 1.5 * 3
W1 = (W2 * 1.5) / 3
Simplifying the equation:
W1 = 0.5W2
Substituting this into the second equation:
(0.5W2 + 10) * 1.5 = W2 * 3
Distributing and simplifying the equation:
0.75W2 + 15 = 3W2
15 = 2.25W2
W2 = 15 / 2.25
W2 ≈ 6.67 kg
Therefore, the weight of the heavier boy is approximately 6.67 kg.
If the weights are x and y, with x > y, then to balance things, we need
x(1) = y(1.5)
(x+10)(1.5) = y(3)
So now just solve for x