A 65-kg boy is sitting on a seesaw 0.6 m from the balance point. How far from the balance point should a 40-kg girl sit so that the seesaw remains balance?
0.975 m
The mass x distance products on the opposte sides must be equal.
65*0.6 = 40*X
Solve for X
To solve this problem, we can use the principle of "lever balance". The total clockwise moment (torque) exerted by the boy's weight on the seesaw must be equal to the total counterclockwise moment exerted by the girl's weight on the seesaw.
The clockwise moment exerted by the boy is calculated by multiplying his weight (65 kg) by his distance from the balance point (0.6 m). Similarly, the counterclockwise moment exerted by the girl is calculated by multiplying her weight (40 kg) by her distance from the balance point (let's call it x).
So, we can write the equation for the moments as follows:
65 kg * 0.6 m = 40 kg * x
Simplifying the equation, we have:
39 kg = 40 kg * x
Dividing both sides by 40 kg, we get:
x = 39 kg / 40 kg
x = 0.975 m
Therefore, the girl should sit 0.975 meters (or approximately 97.5 centimeters) from the balance point in order to keep the seesaw balanced.
To find the distance from the balance point where the 40-kg girl should sit, we need to consider the weight and distance of both the boy and the girl.
Let's assign some variables:
- Let's call the distance of the boy from the balance point x (in meters).
- Let's call the distance of the girl from the balance point y (in meters).
Now, we can use the principle of moments to solve the problem. The principle of moments states that to remain balanced, the product of the weight and distance from the balance point on one side of the axis must be equal to the product on the other side of the axis.
Mathematically, we can express this as:
Weight of the boy × Distance of the boy from the balance point = Weight of the girl × Distance of the girl from the balance point
Or:
(65 kg) × (0.6 m) = (40 kg) × y
Now, let's solve for y:
(65 kg) × (0.6 m) = (40 kg) × y
39 kg·m = 40 kg × y
39 kg·m = 40 kg × y
39 kg·m / 40 kg = y
Calculating this, we find:
y ≈ 0.975 m
Therefore, the 40-kg girl should sit approximately 0.975 meters (or 97.5 centimeters) from the balance point to keep the seesaw balanced.