Step-by-Step Method to Find Mass with 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:
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.
The edge of the knife should be very sharp, and a clear knife-edge pivot should be used.
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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Any bluntness, rust, or dirt in the pivot can cause variations in these two lengths. Therefore, inaccuracy in the measurements.
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.
The body should be placed in the center of the pan to obtain accurate measurements.
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.
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:
Beam balance
Weight box
Forceps
Two objects of different masses
Procedure:
Firstly, adjust the beam balance.
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.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
Students know the working principle of a beam balance.
They learned about the sensibility of the beam balance.
FAQs on How to Determine the Mass of Two Objects Using a Beam Balance
1. What is the working principle of a beam balance used to measure mass?
A beam balance operates on the Principle of Moments. This principle states that for the beam to be in equilibrium (perfectly horizontal), the total clockwise moment about the fulcrum must be equal to the total anticlockwise moment. Since the beam balance has arms of equal length, when the unknown mass on one pan is balanced by standard masses on the other, their masses are equal because the effect of gravity (g) cancels out on both sides.
2. What are the key components of a physical or beam balance?
A typical physical or beam balance consists of several important parts that ensure its accuracy. These include:
- A rigid beam that pivots at the center.
- A central fulcrum, usually a sharp knife-edge, to minimise friction.
- Two pans suspended at equal distances from the fulcrum, one for the object and one for the standard weights.
- A pointer attached to the beam that moves over a scale to indicate when the beam is level.
- Levelling screws at the base to ensure the apparatus is perfectly horizontal.
- A plumb line to verify that the balance stand is vertical.
3. What are the steps to accurately determine the mass of an object using a beam balance?
To accurately measure mass using a beam balance as per the CBSE 2025–26 syllabus guidelines, follow these steps:
1. Adjust the levelling screws to make the base horizontal and ensure the plumb line hangs vertically.
2. Raise the beam and determine the resting point of the pointer on the scale without any weights.
3. Gently place the object to be measured on the left pan.
4. Place a standard weight box on the right-hand side and start adding weights to the right pan, beginning with larger weights and moving to smaller ones.
5. Adjust the weights until the pointer oscillates equally on both sides of the initial resting point.
6. Carefully sum up the masses of all the standard weights on the right pan. This total represents the mass of the object.
4. How do you use a single set of standard weights to compare the masses of two different objects with a beam balance?
To compare the masses of two different objects, you perform two separate measurements. First, place the first object on the left pan and find its mass (m₁) by balancing it with standard weights from your weight box. Record this mass. Next, remove the first object and the weights. Place the second object on the left pan and repeat the procedure to find its mass (m₂). You can then directly compare m₁ and m₂ to determine which is heavier or if they are equal.
5. Why does a beam balance measure an object's mass directly, and not its weight?
This is a key concept. A beam balance measures mass, not weight, because it is a comparison device. Weight is a force (Mass × g), where 'g' is the acceleration due to gravity. When the beam is balanced, the gravitational force on the object (m₁g) is balanced by the gravitational force on the standard weights (m₂g). In the balancing equation, the value of 'g' is present on both sides and thus gets cancelled out. This leaves a direct comparison of masses (m₁ = m₂), making the measurement independent of the local gravitational field.
6. What are the common sources of error when using a beam balance, and how can they be minimised?
Several factors can affect the accuracy of a beam balance. The most common errors include:
- Unequal Arm Lengths: If the fulcrum isn't perfectly at the center, it creates error. This can be minimised by weighing the object on one pan, then swapping it with the weights to the other pan and averaging the two results.
- Air Currents: Gentle breezes can disturb the balance. This is minimised by closing the glass case of the balance during measurement.
- Parallax Error: Incorrectly reading the pointer's position on the scale. This is avoided by keeping your eye level directly in front of the pointer.
- Friction: Worn-out or dirty knife-edges can cause friction. Ensure the fulcrum is clean and sharp for best results.
7. How would the result from a beam balance experiment change if it were performed on the Moon?
The result would not change at all. The Moon's gravitational pull is approximately one-sixth of Earth's. While the weight of both the object and the standard weights would be significantly less on the Moon, this reduction applies equally to both sides of the balance. Since a beam balance compares one mass against another and the gravitational constant 'g' cancels out from the equation, the measured mass would be identical to the mass measured on Earth.
8. Besides school labs, what are some real-world applications of a high-precision beam balance?
High-precision beam balances are crucial in various fields where exact mass measurement is vital. Some examples include:
- Jewellery and Bullion: For accurately weighing precious metals like gold, silver, and platinum, where even a tiny error has significant financial implications.
- Pharmaceuticals: In compounding pharmacies and chemical labs to precisely measure active ingredients for manufacturing medicines.
- Scientific Research: Used in physics and chemistry research to measure reactants and products in experiments with high accuracy.
