This document outlines the procedure for solving statical problems in three steps: 1) Draw the figure according to the given conditions 2) Mark all forces acting on the body based on fundamental points about weight, reactions, tensions, and resultants 3) Use the fact that three non-parallel forces must meet at a point to solve for unknowns It also provides an example problem of a sphere resting on two inclined planes to demonstrate applying the procedure. The key details are drawing the system, identifying the forces of weight and reactions, and using the information that pressure on one plane is half of weight to solve for the inclination of the other plane.

1. STATICS (18UMTC31)
II B.SC. MATHEMATICS (SF)
Mrs. P. Kalaiselvi, M.Sc., M.Phil.,
Ms. N. Malathi, M.Sc.,

2. Procedure to be followed in solving any statical problem
Important Theorem: Two TrignometricalTheorem
If D is any point on the base BC of the
triangle ABC such that and ADC = ,
BAD =  and DAC = , then
i) (m+n) cot  = m cot  - n cot 
ii) (m+n) cot  = n cot B - m cot C
n
m
DC
BD


3. Procedure to be followed in solving any statical problem
Step 1:
Draw the figure according to the given
condition.

4. Procedure to be followed in solving any statical problem
Step 2:Mark all the forces acting on the body, bearing in
mind the following fundamental points:
i) The weight of the body acts vertically downwards
through the centre of gravity.
ii) When the body is leaning against a smooth surface,
the reaction on the body is normal to the surface.

5. Procedure to be followed in solving any statical problem
Step 2:
iii) When a rod is resting on a smooth peg, the
reaction of the peg.

6. Procedure to be followed in solving any statical problem
Step 2:
iv) The tension in a light string is the same
throughout its length and this tension is unaffected by the
string passing over smooth pegs or pulleys. If the pulley is
rough, the tension is different on the two sides of the pulley.

7. Procedure to be followed in solving any statical problem
Step 2:
v) The resultant of two equal forces bisects the angle
between them.

8. Procedure to be followed in solving any statical problem
Step 3:
In addition to the above considerations,
we can use the fact that when there are only
three non-parallel forces, they must meet in a
point.
Thus if three forces are in equillibrium
and two of them meet at a point O, the third
force also must pass through O.

9. Example
Consider the following problem
A heavy uniform sphere rests touching two
smooth inclined planes one of which is 600 to
the horizontal. If the pressure on this plane is
one-half of the weight of the sphere, prove that
the inclination of the other plane to the
horizontal is 300

10. Step 1:
600
A
B


11. Step 2:
600
A
B

CRA RB
W

12. Step 2:

13. Step 3:
The forces acing on the sphere are