a boy of mass 40kg and a girl of 30kg play on a see saw of negligible weight.if the boy sits 270cm from the pivot of the see-saw where must the girl sit to make it balance
360
360
40(270)=30(x)
x will be the distance from the pivot to the girl.
To find where the girl must sit on the see-saw to balance it, we need to consider the principle of moments or torque.
The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.
In this case, since the see-saw is balanced, the sum of the clockwise torques is equal to the sum of the anticlockwise torques.
The torque can be calculated by multiplying the weight of an object by its distance from the pivot.
Let's solve the problem step by step:
1. Calculate the torque of the boy: Torque_boy = weight_boy * distance_boy
The weight of the boy is his mass multiplied by the acceleration due to gravity: weight_boy = mass_boy * gravity
Given: mass_boy = 40 kg and distance_boy = 270 cm = 2.7 m
Therefore, torque_boy = (40 kg) * (9.8 m/s^2) * (2.7 m)
2. Since the see-saw is balanced, the torque generated by the girl must be equal and opposite to that of the boy.
Torque_girl = - Torque_boy
Therefore, torque_girl = -((40 kg) * (9.8 m/s^2) * (2.7 m))
3. Rearrange the equation for torque to solve for the distance the girl must sit:
distance_girl = torque_girl / (mass_girl * gravity)
Given: mass_girl = 30 kg
Therefore, distance_girl = -((40 kg) * (9.8 m/s^2) * (2.7 m)) / ((30 kg) * (9.8 m/s^2))
Simplifying the calculation:
distance_girl = -((40 kg) * (2.7 m)) / (30 kg)
After performing the calculation, we get:
distance_girl ≈ -3.6 m
Since distance cannot be negative in this case, we can discard the negative sign, and the girl should sit approximately 3.6 meters from the pivot on the opposite side of the boy to balance the see-saw.