Two children with masses of 18 kg and 36 kg are sitting on a balanced seesaw. If the heavier child is sitting 0.45 m from the center, at what distance from the center is the lighter child sitting?
Answer in units of m. Please help !!!
mass * distance must be equal, so
18x = 36*0.45
.9 m
mass * distance needs to be equivalent,
18x = 36*.45
= .9m
To find the distance from the center at which the lighter child is sitting, we can use the principle of the lever, which states that the clockwise moment is equal to the anticlockwise moment.
In this case, the clockwise moment is the product of the mass of the heavier child, their distance from the center, and the force of gravity (which is equal to the weight, mass multiplied by the acceleration due to gravity).
The anticlockwise moment is the product of the mass of the lighter child, their distance from the center, and the force of gravity.
Since the seesaw is balanced, these two moments must be equal. We can express this mathematically as:
Clockwise moment = Anticlockwise moment
(mass of heavier child) × (distance of heavier child from the center) × (force of gravity) = (mass of lighter child) × (distance of lighter child from the center) × (force of gravity)
We can cancel out the force of gravity on both sides of the equation:
(mass of heavier child) × (distance of heavier child from the center) = (mass of lighter child) × (distance of lighter child from the center)
Now, we can plug in the given values:
mass of heavier child = 36 kg
distance of heavier child from the center = 0.45 m
mass of lighter child = 18 kg
distance of lighter child from the center = ?
Using the equation above, we can solve for the distance of the lighter child:
(36 kg) × (0.45 m) = (18 kg) × (distance of lighter child from the center)
16.2 kg·m = 18 kg × (distance of lighter child from the center)
Divide both sides of the equation by 18 kg:
(16.2 kg·m) / 18 kg = distance of lighter child from the center
0.9 m = distance of lighter child from the center
Therefore, the lighter child is sitting 0.9 meters from the center.