Why Do Equal Torques Keep a Lever in Equilibrium?

[mikefitz]

http://img208.imageshack.us/img208/392/untitledsx2.png

this one seems so simple...i know the answer is 3 and 4; however, I do not know how my book came to that conclusion. can anyone explain to me exactly what is going on in the above diagram? Thanks

 

[radou]

this one seems so simple...i know the answer is 3 and 4; however, I do not know how my book came to that conclusion. can anyone explain to me exactly what is going on in the above diagram? Thanks

Look at each pair of forces and at the pair of torques it would produce. Focus on the magnitudes of the force vectors and on their distance from the axis.

 

[m2003]

In the diagram, we can see that there are two forces acting on the lever arm. The force on the left side is 2N and the force on the right side is 3N. These two forces are acting in opposite directions, but they are also acting at equal distances from the pivot point. This means that they are exerting equal torques on the lever arm.

Torque is a measure of how much force is being applied to an object, taking into account the distance from the pivot point. In this case, the distance from the pivot point to each force is the same, so the forces are exerting equal torques.

To calculate the torque, we multiply the force by the distance from the pivot point. In this case, both forces are acting at a distance of 2 meters from the pivot point, so the torque on the left side is 2N x 2m = 4Nm. Similarly, the torque on the right side is 3N x 2m = 6Nm. Since these two torques are equal, the lever arm is in equilibrium and will not rotate.

In summary, the reason why the answer is 3 and 4 is because the forces are equal in magnitude and acting at equal distances from the pivot point, resulting in equal torques.