Page 42 - Physics - XI

→ → →
Let θ be the angle between the two forces P and Q . Let R be their resultant, then R P Q
→
The magnitude of R is
2
2
R = P + Q + 2 PQcosθ
Mirror strip
B A
→ H →
Q P
G F
O
E
I

J

X

X

Fig. 6.2

Procedure
1. Set up the Gravesand's apparatus in the vertical position with the help of a plumb line and fi x a white
drawing paper sheet on the board with the help of drawing pins.

2. Take a fi ne strong thread of suffi cient length. Tie two hangers, one at each end of the thread. Pass this
thread over the pulleys P and P . Now, tie another shorter string in the middle of the fi rst string to make
2
1
a knot at O, and tie the wooden slab (unknown weight) at its other end as shown in Fig. 6.1.
3. Check the pulleys P and P that they are frictionless, oil them if necessary.
1
2
4. Adjust the weights on the hangers so that the knotted point O lies somewhere in the middle of the
paper. Care should be taken that the hangers do not touch the board or the table. Now, mark point O
just under the knot with a pointed pencil.
→ → →
5. To mark the direction of forces PQ, , and X acting along the string, place a mirror strip below the
string and adjust the position of eye so that there is no parallax between the string and its image in the

glass strip. Now, mark the two points E and F at the edges of the mirror strip where the image of the
string leaves the mirror [Fig. 6.2]. In the same way, mark the directions of the other two forces by the
points G and H and by points I and J along the string.
6. Note the weight of each hanger and slotted weight on the hangers. Now, remove the hangers along with
the weight.

7. Detach the white paper sheet from the board. Join the three pairs of points marked on the paper to meet
at O.
→
8. Choose a proper scale (say 50 g wt = 1.0 cm). From O mark lengths OA and OB to represent forces P
→
and Q acting at the point O. Now, complete the parallelogram OACB taking OA and OB as adjacent
sides.
9. Draw diagonal OC whose length will measure the magnitude of the unknown weight. If OC does not
lie along OX, produce OX to meet BC at C' and measure the angle COC'.

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