Apparatus
Gravesand’s app., Two slotted weights with hanger. Plane mirror strip, Thread, Drawing pins, Plane paper, Protractor, Body of-unknown weight.
Diagram
Point to Ponder
Vectors
Those physical quantities which can be completely described by magnitude as well as specific direction are called vectors. e.g., force, torque, momentum etc.
Vectors can be represented symbolically as well as graphically. Symbolically vectors can be represented by bold face letters i.e., A, B, C or simple letter with an arrow head above or below the letter . Graphically a vector is represented by an arrow which drawn according to suitable scale.
Resultant Vector
The resultant (sum) of number of similar vectors is that single vector which have the same effect as the combine effect of the all original vectors taken together.
Resolution of a Vector
The process of splitting a vector into its components is called resolution of vector. It is the reverse process of addition of vectors. In resolution of a vector a single vector along with its direction is converted into two or more components.
Let us consider two forces P and Q which are acting in different direction on a body to get the resultant of these forces we resolve them, so that we get its x-components and y-components.
Adding the x-components
Rx = Px + Qx
Rx = P cos 1 + (-Q cos 2)
P = Q and 1 = 2
Rx = P cos 1 – P cos 1
Rx = 0
Similarly adding y-components
Ry = Py + Qy
Ry = P sin 1 + Q sin 2
Equilibrium
If the sum of all the force acting on a body or it moves with uniform velocity then it is said to in equilibrium. There are two types:
(1) Static Equilibrium
If the body is at rest then it is said to be in static equilibrium.
(ii) Dynamic Equilibrium
If a body is moving with uniform velocity then it is said to be in dynamic equilibrium.
Using conditions of equilibrium.
Now according to first condition of equilibrium EF = 0.
Upward force = Down word force
R = P sin 1 + Q sin 2 = W
W = P sin 1 + Q sin 2
Procedure
Test the pulleys for no friction by revolving them. Set the Gravesand’s apparatus exactly vertical by a plumb line. Take a piece of thread and attach two hangers at its two ends. Take another piece of thread and attach the given body of unknown weight with it. Now put equal slotted weights on both hangers, and level them. Tie the thread of body of unknown weight in middle between two pulleys. This arrangement looks like Y shape. Fix a sheet of paper on board such that knot lies in the middle of paper.
See that the weights do not touch the board. Place mirror strip under each thread one by one and mark two points on the paper on both sides of strip when thread and its image just cover each other. B removing weights, join the marks by drawing straight lines which meet at point O. Draw a horizontal line passing through point O. Select a suitable scale and cut off line OA and OB which represent forces P and Q. Draw perpendiculars from A and B on x-axis. Rectangular components are Px = P cos 1, Py = sin 1 and Qx = Q cos 2, Qy = sin 2. Forces Px and Qx are acting in opposite direction and also point ‘O’ is in equilibrium, they must cancel each other. Both Py and Qy, are directed upward. Their sum give resultant R = P sin 1 + Q sin 2. As knot is in equilibrium, therefore W = R, which is weight of the body.
Observations and calculations:
Mean W = ………. N
Result
Unknown weight = W = …………. N
Exercise
Find known weight of a body by the method of vector addition of forces (Graphical method OR Head to Tail rule).
Precautions
(1) Pulleys should be frictionless.
(2) Board should be vertical.
(3) Hangers should not touch the board.
(4) Knot should be in the center of paper.
(5) Arrow head must be put at the end of rectangular compounds.
VIVA VOCE
Q.1 What do you mean by rectangular components?
Ans. The compounds of a vector which are perpendicular to each other are called rectangular components.
Q.2 What is resultant vector?
Ans. It is a single vector which has the same effect as the combined effect of two or more vectors.
Q.3 Find the unknown weight W, by using following observation diagram using concept of equilibrium.
Ans. In equilibrium:
W = T1 sin 60 + T2 sin 20
= 50 + 2
= 77 N
Unknown weight = W = 77 N
