A boy who weighs 30 kilograms sits on one end of a seesaw. On the other end there is a girl who weighs 20 kilograms. The girl is 1.5 metres from the fulcrum. How far from the fulcrum must be the boy sit in order to balance the seesaw? How far away must the boy sit if the girl is 3 metres from the fulcrum? What conclusion can you make about the seesaw?
the moments about the fulcrum must be equal for balance
moment = mass * distance from fulcrum
To solve this problem, let's 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 about a fulcrum must equal the sum of the counterclockwise moments about the same fulcrum.
In this case, we have a seesaw with a boy of 30 kilograms on one end and a girl of 20 kilograms on the other end. Let's assume the seesaw is balanced when the boy is x meters away from the fulcrum.
First, let's find the clockwise and counterclockwise moments. Since the weight of an object is equal to its mass multiplied by the acceleration due to gravity (9.8 m/s^2), the clockwise moment is the product of the girl's weight (20 kg * 9.8 m/s^2) and the distance from the fulcrum (1.5 meters).
Clockwise moment = 20 kg * 9.8 m/s^2 * 1.5 m
Similarly, the counterclockwise moment is the product of the boy's weight (30 kg * 9.8 m/s^2) and the distance from the fulcrum (x meters).
Counterclockwise moment = 30 kg * 9.8 m/s^2 * x
According to the principle of moments, these two moments should be equal for the seesaw to be balanced. So, we can set up the equation:
Clockwise moment = Counterclockwise moment
20 kg * 9.8 m/s^2 * 1.5 m = 30 kg * 9.8 m/s^2 * x
Now we can solve for x:
20 kg * 9.8 m/s^2 * 1.5 m = 30 kg * 9.8 m/s^2 * x
294 kg·m = 294 kg·m
Here, we see that the equation is balanced. Therefore, the seesaw is balanced when the boy is 1.5 meters away from the fulcrum.
Now let's find the distance from the fulcrum if the girl is 3 meters away. We can use the same equation:
20 kg * 9.8 m/s^2 * 3 m = 30 kg * 9.8 m/s^2 * x
Now we can solve for x:
588 kg·m = 294 kg·m
Again, we see that the equation is balanced. Therefore, the seesaw is also balanced when the boy is 3 meters away from the fulcrum.
In conclusion, the seesaw is balanced if the boy sits 1.5 meters away from the fulcrum when the girl is 1.5 meters away, and the seesaw is also balanced if the boy sits 3 meters away when the girl is 3 meters away. Thus, we can conclude that the seesaw is symmetric and obeys the principle of moments.