Aim
To find the weight of a given body using parallelogram law of vectors.
Materials Required
- Gravesand’s apparatus which is a parallelogram law of forces apparatus
- Plumb line
- Two hangers with slotted weights
- A body whose weight is to be determined
- Thin strong thread
- White drawing paper
- Drawing pins
- Mirror strip
- Sharp pencil
- Half-meter scale
- Set squares
- Protractor
Theory
If an unknown weight body S is suspended from the middle of the hanger, and P and Q are the two balance weights from the other two ends of the hanger, then the unknown weight is calculated using the below equation:
\(S=\sqrt{P^{2}+Q^{2}+2PQcos\theta }\) |
Where,
- S is the unknown weight
- P and Q are the balance weights
Diagram
Procedure
- Set up the Gravesand’s apparatus with its board verticle with the help of a plumb line.
- Oil the pulleys P_{1} and P_{2} if they are not frictionless.
- With the help of drawing pins, fix the white sheet on the board.
- Let O be the knot made from three-piece of strong thread.
- Let P and Q be the be the weights that are tied at both the ends of the hanger and S be the given body tied to the third end.
- Let the third weight S be vertically in the middle of the board and weights P and Q are passed over the pulley.
- Junction O should be maintained at equilibrium by adjusting weights P and Q.
- All the three weights P, Q and S act as three forces \(\underset{P}{\rightarrow}\), \(\underset{Q}{\rightarrow}\) and \(\underset{S}{\rightarrow}\).
- All three weights should hang freely without touching the board or table.
- With a sharp pencil, mark the position of junction O.
- Disturb the weights P and Q and leave them free.
- The position of junction O will be closer to the earlier position.
- Let P_{1} and P_{2 }be the position of P, Q_{1} and Q_{2 }be the position of Q and S_{1 }and S_{2} be the position of S which are taken down with the help of the mirror.
- Remove the paper from the board.
- Using half-meter scale draw lines through P_{1} and P_{2}, Q_{1} and Q_{2} and S_{1} and S_{2 }represent P, Q, and S respectively. All these lines should meet at point O.
- Taking a scale, 1 cm = 50 g, OA = 3 cm and OB = 3 cm to represent P =150g and Q = 150g.
- R is represented by completing the parallelogram OACB and by joining OC with the help of set squares.
- When OC is measured, it comes to 3.9 cm.
- P and Q can be changed for different sets.
- By using spring balance, find the weight of the wooden box.
Observation
Least count of spring balance = …… g
Zero error of spring balance = …….. g
Weight of unknown body by spring balance = …….g
Scale used: Let 1 cm = 50 g
Sl. no |
Forces |
Sides |
Resultant force R (g wt) |
Unknown weight S (g wt) |
Weight by spring balance (g wt) |
Error (g wt) |
|||
P (g wt) |
Q (g wt) |
OA (cm) |
OB (cm) |
OC (cm) |
|||||
1. |
150 |
150 |
3 |
3 |
3.9 |
195 |
195 |
200 |
5 |
2. |
|||||||||
3. |
Calculations
OC = 3.9 cm, R = 50 × 3.9 = 195g
Unknown weight, S = 195g
Mean unknown weight, \(S=\frac{S_{1}+S_{2}+S_{3}}{3}\) = 195g
Weight by spring balance = 200g
Difference = 5g
Result
The unknown weight of given body = 195g
The error is within limits of experimental error.
Precautions
- The board should be stable and placed verticle.
- There shouldn’t be any friction in the pulleys.
- The board or the table should not be in touch with the hangers.
- The middle of the paper should have junction O.
- When the weights are at rest, the points should be marked.
- A sharp pencil should be used to mark the points.
- To show the direction of forces, arrows should be marked.
- To make a fairly big parallelogram, a proper scale should be taken.
Sources Of Error
- There might be friction in the pulleys.
- Weights might not be accurate.
- Points marked may be correct.
- Weight measured by spring balance may not be accurate.
Viva Questions
Q1. Define scalar quantity.
Ans: It is defined as the physical quantity which has only magnitude like length, mass, etc.
Q2. Define vector quantity.
Ans: It is defined as the physical quantity which has magnitude and direction like force, velocity, etc.
Q3. Define addition of vector.
Ans: Addition of vector is defined as the operation of adding two or more vectors together into a vector sum.
Q4. What is resolution of vectors?
Ans: Resolution of the vector is defined as the breaking of a single vector into its components.
Q5. Why is addition of vector different from addition of scalars?
Ans: Addition of vector has direction and magnitude whereas addition of scalar has only magnitude. Therefore, the addition of vector is different from the addition of scalar.
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