Parallelogram law
Aim To find the weight of a given body using parallelogram law of vectors.
Apparatus:
1. Gravesand’s apparatus which is a parallelogram law of forces apparatus
2. Plumb line 3. Two hangers with slotted weights 4. A body whose weight is to be determined 5. Thin strong thread 6.
White drawing paper 7. Drawing pins 8. Mirror strip 9. Sharp pencil 10. Half-meter scale 11. Set squares 12. Protractor
Theory
If an unknown weight body S is suspended from the middle of the hanger, P and Q are the two balance weights from the
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other two ends of the hanger, then P~ + Q + S . = 0
the unknown weight is calculated using the below equation:
p
R = P 2 + Q2 + 2P Qcosθ
Where, S is the unknown weight, P and Q are the balance weights
Procedure
1. Set up the Gravesand’s apparatus with its board verticle with the help of a plumb line.
2. Oil the pulleys P1 and P2 if they are not frictionless.
3. With the help of drawing pins, fix the white sheet on the board.
4. Let O be the knot made from three-piece of strong thread.
5. 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.
6. Let the third weight S be vertically in the middle of the board and weights P and Q are passed over the pulley.
7. Junction O should be maintained at equilibrium by adjusting weights P and Q.
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8. All the three weights P, Q and S act as three forces P~ , Q and S .
9. All three weights should hang freely without touching the board or table.
10. With a sharp pencil, mark the position of junction O.
11. Disturb the weights P and Q and leave them free.
12. The position of junction O will be closer to the earlier position.
13. Let P1 and P2 be the position of P, Q1 and Q2 be the position of Q and S1 and S2 be the position of S which are taken
down with the help of the mirror.
14. Remove the paper from the board.
15. Using half-meter scale draw lines through P1 and P2 , Q1 and Q2 and S1 and S2 represent P, Q, and S respectively.
All these lines should meet at point O.
.
16. Taking a scale, 1 cm = 50 g, OA = 3 cm and OB = 3 cm to represent P weight and Q weight
17. R is represented by completing the parallelogram OACB and by joining OC with the help of set squares.
18. Measure OC length.
19. P and Q can be changed for different sets.
20. By using spring balance, find the weight of the unknown weight.
Observation
Least count of spring balance = . . . . . . g
Zero error of spring balance = . . . . . . .. g
Scale used: Let 1 cm = 50 g
Table:
S. No
1
2
3
Forces
P(g wt) Q(g wt)
OA(cm)
Sides
OB(cm)
OC(cm)
Resultant force
R(g wt)
Calculations
R = 50 × oc length = ____g
Unknown weight, S = ____g
Mean unknown weight, S=(S1+S2+S3)/3 = ___g
Difference in real weight to measured weight = ___g
Result
The unknown weight of given body = ____g
The error is within limits of experimental error.
Precautions
1. The board should be stable and placed verticle.
2. There shouldn’t be any friction in the pulleys.
3. The board or the table should not be in touch with the hangers.
4. The middle of the paper should have junction O.
5. When the weights are at rest, the points should be marked.
6. A sharp pencil should be used to mark the points.
7. To show the direction of forces, arrows should be marked.
8. To make a fairly big parallelogram, a proper scale should be taken.
Sources Of Error
1. There might be friction in the pulleys.
2. Weights might not be accurate.
3. Points marked may be correct.
Unknown
weight S (g wt)
Real
weight
Error(g wt)