A boy of mass 40kg and a girl of mass 30kg play on seesaw of negligible weight if the boy sits 3m from the pivot where must the girl sit to balance
Well, if the boy is sitting at 3m from the pivot, we can consider his torque as a counter-clockwise force acting on the seesaw. To balance the seesaw, we need to find the position where the girl must sit.
Given that the boy's mass is 40kg and girl's mass is 30kg, we can calculate the torque generated by the boy using the formula:
Torque = force × distance
Since torque is directly proportional to the distance from the pivot, the torque generated by the boy is 40kg × 3m = 120kgm.
To balance the seesaw, the girl's torque must be equal to the boy's torque, but in the opposite direction (clockwise) since they cancel each other out. So, we can set up the equation:
Girl's torque = -120kgm
To find the position where the girl must sit, we can rearrange the equation:
Force × distance = -120kgm
Since the girl's mass is 30kg, the equation becomes:
30kg × distance = -120kgm
Solving for distance:
distance = -120kgm / 30kg
Now, since distance can't be negative in this case, we can ignore the negative sign:
distance = 120kgm / 30kg
distance = 4m
Therefore, the girl must sit 4m from the pivot to balance the seesaw with the boy.
To balance a seesaw, the torques on both sides of the pivot point must be equal. Torque is calculated by multiplying the force applied by the distance from the pivot point.
In this case, the torque exerted by the boy is equal to the torque exerted by the girl. Since the seesaw's weight is negligible, we need to consider only the weights of the boy and the girl.
Torque exerted by the boy = force of weight of the boy x distance from the pivot point
Torque exerted by the girl = force of weight of the girl x distance from the pivot point
Since the torques are equal, we can set up an equation to find the distance at which the girl must sit:
(Weight of boy)(Distance from boy to pivot) = (Weight of girl)(Distance from girl to pivot)
Substituting the given values:
(40 kg)(3 m) = (30 kg)(Distance from girl to pivot)
Rearranging the equation, we can solve for the distance from the girl to the pivot:
Distance from girl to pivot = (40 kg)(3 m) / (30 kg)
Calculating the value, we find:
Distance from girl to pivot = 120 m / 30 kg = 4 m
Therefore, the girl must sit at a distance of 4 meters from the pivot point in order to balance the seesaw.
To balance the seesaw, the torques on both sides of the pivot point must be equal. Torque is given by the formula:
Torque = Distance × Force
In this case, the force is the weight of the person and the distance is the distance from the pivot.
Let's calculate the torque for both the boy and the girl:
Torque_boy = 40kg × 9.8m/s² × 3m
Torque_girl = 30kg × 9.8m/s² × x
To balance the seesaw, the torques must be equal:
40kg × 9.8m/s² × 3m = 30kg × 9.8m/s² × x
Simplifying the equation:
3 × 40kg × 9.8m/s² = 30kg × 9.8m/s² × x
1176 = 294 × x
Dividing both sides by 294:
x = 1176 / 294
x = 4m
Therefore, the girl must sit 4m from the pivot to balance the seesaw with the boy.