Johnny gets some Torque with Jane on the See-Saw

jane johnny
 
Johnny sees a girl standing by the monkey bars. Her name is Jane, and Johnny thinks it would be a good idea for her to join play with him on the see-saw. If both children sit on either end of the see-saw, which end will go down, and why?
seesaw
A see-saw is an example of a simple lever. At the center of the see-saw, balancing either side is the fulcrum. The fulcrum serves as an axis of rotation for the see-saw.

The two arms of the see-saw are called the lever arms. A lever arm is defined as the distance between the axis of rotation and the line of action. The line of action is a line that is perpindicular to the point at which the force is exerted. On this see-saw, Johnny sits on one of the lever arms, while Jane sits on the other.

The force pushing down on the two children is force of gravity. So if Johnny's mass is greater than Jane's mass, there will be a greater force pushing down on Johnny's lever arm.


If the length of the lever arm is the same for the two children, it can be concluded that Jane's mass is exerting a greater torque than Johnny's. Torque is defined as the magnitude of the force times the lever arm, and is explained by the equation:
T = Fl
where T = torque (N*m), F = Force (N), and l = the length of the lever arm (m).
seesaw1 This example of torque is a simple one because the force is in a plane perpindicular to the axis of rotation. However, if you place unequal forces on a see-saw, it does not always stay horizontal, as Johnny and Jane soon found out.


For the see-saw to stay horizontal, that is to stay in equilibrium, the net torque would have to equal zero:
equation


So how exactly do we know which side of the see-saw will go up, and which side will go down? To understand this, we can find the net torque of the see-saw.


First, we have to find the torque acting on each lever arm.

Johnny and Jane are sitting an equal distance of 1 meter from the axis of rotation. Johnny has a mass of 20 kg, and Jane has a mass of 22 kg. The force in this problem is the force the weight of an object on earth, or W=mg, where m is mass and g is acceleration due to gravity (9.8m/s²).


Torque acting on Johnny's side of the see-saw:

        T = Fl
        T = (22 kg)(9.8 m/s²)(1 m)
        T = 215.6 N*m

Torque acting on Jane's side of the see-saw:

        T = (20 kg)(9.8 m/s²)(-1 m)
        T = -196 N*m

Net Torque acting on the see-saw:

        215.6 N*m + -196 N*m
        = 19.6 N*m

Because the net torque of the see-saw is positive, Johnny will be in the air, and Jane will still be on the ground. If the net torque was negative, it would be the opposite scenario.