Objective

The goal of this experiment is to determine the weight of a specific object using the parallelogram law of vectors.

Necessary Equipment

1. Gravesand’s apparatus, also known as a parallelogram law of forces apparatus
2. A plumb line
3. Two hangers equipped with slotted weights
4. The object whose weight needs to be found
5. A durable, thin thread
6. A sheet of white drawing paper
7. Drawing pins
8. A strip of mirror
9. A sharp pencil
10. A half-meter scale
11. Set squares
12. A protractor

Theoretical Background

If an object with an unknown weight S is suspended from the middle of the hanger, and P and Q are the two balancing weights on the other ends of the hanger, then the unknown weight is determined using the following equation:

In this equation,

• S is the unknown weight
• P and Q are the balancing weights

Illustration

Experimental Procedure

1. Arrange the Gravesand’s apparatus vertically using the plumb line.
2. If the pulleys P ₁ and P ₂ are not frictionless, apply some oil.
3. Use drawing pins to fix the white sheet on the board.
4. O is the knot created from three pieces of strong thread.
5. P and Q are the weights tied to the two ends of the hanger, and S is the object tied to the third end.
6. Suspend the weight S vertically in the center of the board and pass weights P and Q over the pulley.
7. Maintain the junction O at equilibrium by adjusting weights P and Q.
8. The three weights P, Q, and S act as three forces,
   \(\begin{array}{l}\overrightarrow{P}, \,\, \overrightarrow{Q}\,\, \textup{and} \,\, \overrightarrow{S}.\end{array} \)
9. Make sure the three weights hang freely without touching the board or table.
10. Mark the position of junction O with a sharp pencil.
11. Disturb the weights P and Q and then leave them free.
12. The position of junction O will return close to its original position.
13. Record the positions of P, Q, and S with the help of the mirror.
14. Remove the paper from the board.
15. Draw lines through the recorded positions to represent P, Q, and S. All these lines should meet at point O.
16. Use a scale, where 1 cm = 50 g, to represent P =150g and Q = 150g.
17. Complete the parallelogram OACB and join OC to represent R.
18. Measure OC, which should be 3.9 cm.
19. Change P and Q for different sets.
20. Use a spring balance to find the weight of the object.

Observations

Least count of spring balance = …… g

Zero error of spring balance = …….. g

Weight of unknown object by spring balance = …….g

Used scale: 1 cm = 50 g

Results

The discovered weight of the given object = 195 g

Any error falls within the acceptable range for experimental error.

Safety Measures

1. The board must be stable and placed vertically.
2. The pulleys should be frictionless.
3. The hangers should not touch the board or the table.
4. The junction O should be in the center of the paper.
5. Mark the points only when the weights are at rest.
6. Use a sharp pencil to mark the points.
7. Mark arrows to indicate the direction of forces.
8. Choose a suitable scale to create a large enough parallelogram.

Potential Errors

1. There might be friction in the pulleys.
2. The weights might not be accurate.
3. The marked points may be incorrect.
4. The weight measured by the spring balance may not be accurate.

Learn More: Vector Addition