Unit 2 & 3 Project

How are the principles of rotational equilibrium applied in triple beam balance?

Torque is a twisting force that causes rotational motion. When an object is in rotational equilibrium, it is not moving or rotating, thus the net sum of torque on the object equals to zero and the sum of the clockwise torques must be equal to the sum of the counter clockwise torques.

A real life application of rotational equilibrium can be found in triple beam balance.
A triple beam balance is a type of balance commonly used in schools, offices and laboratories to determine the mass of samples. A triple beam balance works by matching the torque resulting from the measured mass with an adjustable torque generated by balancing masses.

If you would like to measure the mass of an object using a triple beam balance, you first have to adjust the balance so it will point at the number zero. Then you place the object on the pan. Afterwards, you adjust the sliding weights called riders on the three beams, so the pointer will once again, point at zero. Once the Triple Beam Balance is balanced, you look at the riders and see what numbers they are on. That is the mass.

Here is a short video demonstrating how to use a triple beam balance

http://www.youtube.com/watch?feature=player_embedded&v=FfuBO3-K8AQh

A triple beam balance works on the principles of torque and rotational equilibrium.

Basically, if the two forces on each side of the balance point (pivot) are equal, the balance will be horizontal and it will be in equilibrium. The pointer on the balance indicates this condition. The object being weighed has a specific mass generating a fixed torque at its fixed position. The torque exerted by the riders on the other side of the pivot can be varied according to the position of the sliding weights on the beam.

These positions have been calibrated to correspond to specific weights, so when each side is balanced you can read the weight that is balanced against the object.

To be completely scientific, we are measuring torque when we use a balance beam. The amount of torque on each side will be equivalent when the beam is balanced.
Torque is calculated using the formula below:

where:
r is the distance from the pivot to the point where force is applied
F is the magnitude of the force,

As the riders move further away from the pivot, they exert a greater downward force on the beam and upward force on the pan. If the beam is balanced, it indicates that the sample and the riders exert the same magnitude of forces and therefore their masses equal since gravity is constant.

While a spring scale measures the weight of an object, a triple beam balance measures the true mass of an object, and not just weight that changes with changing gravitational force. This is because the force that is acting on each side of the pivot of the balance is gravitational force. Gravity will be constant wherever you are, only moment or torque will be relevant.

Bibliography

Torque, Wikipedia, http://en.wikipedia.org/wiki/Torque

Weighing scale, Wikipedia, http://en.wikipedia.org/wiki/Weighing_scale

Class notes