To Determine the Mass of Two Different Objects Using a Beam Balance

What is a Beam Balance?

A beam balance is a device used to determine the mass of objects under gravitation.

The arrangement of the system is in such a way that a beam is supported at the center by an agate knife-edge resting on a support moving inside a vertical pillar.

This beam carries a light point that moves over a scale.

This device is used for calibrating masses in the range of 10 mg and 1 kg.

There are two stirrups at the ends of the beam that carry two scale pans of equal masses along with adjusting nutcase. 

These nuts can be adjusted to make the pointer oscillate within the scale when the balance is raised. The balance is affixed on a platform provided with three leveling screws,  which make the pillar vertical. 

There is a plumb line that shows whether the pillar is vertical or not, and is placed just above the pointed projection.

The beam balance is enclosed in a glass case to avoid disturbances due to air.

To Determine the Mass of Two Different Objects Using a Beam Balance

There are some important instructions to determine the mass of the objects using beam balance that is outlined below:

1. The measurement accuracy and resolution achieved depends upon the quality and sharpness of the knife-edge that the pivot is formed from. It means to get the high-resolution measurement, friction at the pivot must be as close to zero as possible.

2. The edge of the knife should be very sharp, and a clear knife-edge pivot should be used.

3. The two-halves of the beam on either side of the pivot must be of equal length and be measured from the knife edge.

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4. Any bluntness, rust, or dirt in the pivot can cause variations in these two lengths. Therefore, inaccuracy in the measurements.

5. Make sure that all the knife edges on the beam balance are parallel because these two pans are hung from the knife-edge, and the displacement of the point of application of the force over the line of the knife-edge can cause measurement errors.

6. The body should be placed in the center of the pan to obtain accurate measurements.

7. Therefore, greater care is required in the use of such instruments, particularly in regard to keeping the knife edges sharp and clean, so that a high-measurement accuracy is achievable.

8. We need to keep the instrument exactly in balance, and such a good condition can be achieved by applying calibrated masses to each side of the balance.

So, these are the instructions to be kept in mind to achieve the exact measurement.

Determine Mass of Two Different Objects Using Beam Balance

Aim:

To find the mass of a given body/object by sensibility method, by using a beam balance.

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Materials Required:

1. Beam balance

2. Weight box

3. Forceps

4. Two objects of different masses

Procedure:

1. Firstly, adjust the beam balance. 

2. When the beam is in a raised position, the pointer will stay at rest and coincide with the zero division or oscillates about the zero division. When the beam comes to rest, put any one of the objects in the left pan. Then, put a standard weight with the half of forceps from the weight box, and then shut the front glass door, so that there is no air disturbance. Then, raise the beam with the help of a handle and notice that the beam is horizontal, and the pointer is oscillating equally on both sides of zero division.
   If not, then adjust by adding or removing a few fractional weights to get the correct horizontal position of beam and pointer. Bring the beam to rest, then collect all the weight and add them, which give the gravitational mass of the object. Now remove the object from the left pan.

3. Repeat the Step-2 for the second object.

Theory of Beam Balance

A physical balance, such as beam balance determines the gravitational mass of a body by using the principle of moments.

 m₁g x a₁ = m₂g x a₂               

A body of gravitational mass m₁ is placed on the left pan of the balance, while a body with a standard weight of gravitational mass m₂ on the right pan to keep the beam horizontal for a beam balance, such that a₁ = a₂.

Then, m₁ = m₂

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It means that the gravitational mass m₁ of the body in the left pan  =  gravitational mass m₂ of the standard weight in the right pan.

Therefore, the correct mass of the body using the beam balance,

M = W + (R - R₀)S

Here, W = mass in the pan

R₀ = zero resting point

R =Resting point with the object that is counterbalanced with weight W

S = sensibility of the balance

The sensibility and the weight required to shift the resting point by one division can be calculated from the equation,

Here, R₁ = Resting point with 10 mg in the right pan

  Learning outcomes

1. Students know the working principle of a beam balance.

2. They learned about the sensibility of the beam balance.