Person A has a mass of 50kg and decides to sit 5 m to the left of the fulcrum on a see-saw. Person B has a mass of 100kg and decides to sit 10 m to the left of the fulcrum on a see-saw. Determine the distance of a -person having a mass of 200 kg, if this person sits on the right side of the see-saw to make it horizontally balanced.
To determine the distance at which a person with a mass of 200 kg should sit on the right side of the seesaw to balance it horizontally, we need to apply the principle of moments.
The principle of moments states that for an object to be in rotational equilibrium, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments. In this case, we can consider the fulcrum of the seesaw as the pivot.
Let's calculate the moments for each person:
For Person A:
Mass of Person A (m1) = 50 kg
Distance of Person A from the fulcrum (d1) = 5 m
Moment of Person A (M1) = m1 * d1 = 50 kg * 5 m = 250 kg∙m
For Person B:
Mass of Person B (m2) = 100 kg
Distance of Person B from the fulcrum (d2) = 10 m
Moment of Person B (M2) = m2 * d2 = 100 kg * 10 m = 1000 kg∙m
To balance the seesaw horizontally, the sum of the moments on either side of the fulcrum must be equal:
M1 = M2
250 kg∙m = 1000 kg∙m
Now, let's solve for the distance (d3) at which a person with a mass of 200 kg should sit on the right side of the seesaw:
Mass of the new person (m3) = 200 kg
Moment of the new person (M3) = m3 * d3
Since the seesaw is in balance, the total counterclockwise moment (M3) would be equal to the total clockwise moment (M1 + M2).
M3 = M1 + M2
200 kg * d3 = 250 kg∙m + 1000 kg∙m
200 kg * d3 = 1250 kg∙m
d3 = (1250 kg∙m) / 200 kg
d3 = 6.25 m
Therefore, a person with a mass of 200 kg should sit approximately 6.25 meters from the fulcrum on the right side of the seesaw to balance it horizontally.