This problem deals with torque and equilibrium. Noting that the string is between the two masses we can use the torque equation of . We can use the equation to find the torque. Since force is perpendicular to the distance we can use the equation  (sine of 90^o is 1). Force presented in this situation is gravity, therefore F=mg, and using the variable x as a placement for the string we can find r.

x=43, thus the string is placed at the 43cm mark.

We are trying to find what force needs to be applied to the rope to result in a net of zero torque on the beam.

Torque applied by the car:

We can use this to find the mass of a student that will create the same amount of torque while hanging from the rope:

Torque is defined as . In this case, is zero because Bob and the weight are sitting directly on top of the seesaw; all of their weight is projected directly downward. Therefore, the torque that the weight applies is:

In order for the seesaw to balance, the torque applied by Bob must be equal to .

Magnitude of torque can be found by relating the amount of force applied perpendicular to a lever arm about a point of rotation.

In this case, the force is not perpendicular, so we must take the perpendicular aspect of the force to find torque.

Plug in and solve.

To calculate the torque experienced by the object, we must take the cross product of the force vector and the position vector.

The definition of torque is

 Where

 is the force

 is the distance

Theta is the angle between the direction of the force and the distance.

In this case, , so  .

Plugging in our remaining values:

Initial angular momentum is zero

Combine equations:

Solve for

Definition of :

Combine equations:

Plug in values:

The torque  is produced by a force  acting at a radius . Since the force and the radius are perpendicular, then the torque equation gives us:

The new torque, which we will call  is produced by a force of  acting at a radius of  at an angle of . Thus the torque equation gives us:

Since , plugging this in to the above gives us 

Torque is given by:

, where  is the length of the rod from the pivot point,  is the force acting on the rod, and  is the angle. Since we have all of these components, we can plug in and solve:

A system will only have a net torque of 0 when it has no net force or the net force goes through its center of gravity. The only forces applied in this system is from gravity. Therefore, we need to find the orientation at which all gravitational force goes through point p. This occurs when the rod is oriented vertically, thus . 

Note:  will also result in a net torque of 0. At this orientation, the rod is also vertical with the masses in swapped positions.