Centre Of Gravity and Stability of bodies

1.         ---CH.7---Centre of Gravity            And Stability of bodies Done by Jinsi Hirpara ,vii cm 1b

2. What do you mean by WEIGHT??? • Note: In physics , Mass and weight are totally different. • The gravitational force pulling the objects towards the center of earth is known as WEIGHT. • Weight can also be defined using the formula -   • Weight = mass x acceleration due to gravity • W = mg • Since weight is the force pulling objects towards itself , it can also be said that it always acts in downward direction.                                                     

3. Derivation of F = Mg Masses of particles = m1,m2,m3,….                                                                                      Resultant 'F' = F1,F2,F3,…                                                                                      F = m1g + m2g + m3g + …..                                                                                      If we take 'g' common                                                                                      F = g(m1 + m2 +    m3 + …...)                                                                                      M = m1 + m2 + m3 + …..                                                                                       F = g(M)                                                                                       F = Mg

4. Centre of Gravity • The center of gravity is the average location of the weight of an object.                                                   OR    • Centre of gravity is the point through which the resultant of the weight of all the particles of the body acts. OR • Center of gravity of a body is a special point where the entire weight of the body appears to act. •  The center of gravity depends upon the shape and mass distributed in it . • Center of gravity (C.G) of a body can be inside or outside of the body. • The position of the center of gravity of a given body depends on its shape and the distribution of mass in it.

6. Line of action : The imaginary line showing the direction of this resultant force .i.e. It is the vertical line which goes through the base of the body and helps to indicate the Centre of gravity of the body.  Line of Action *The line of action in a stable bodyalways passes through the base of the body. * The line of action in an unstable body always falls outside the base of the body.Eg:Hollow Bodies(stool,tripod,ring, boomerang,etc Centre Of Gravity

7. Where is the position of Centre of gravity in Regular Bodies??? • The position of Centre of gravity of the regular bodies is on the center of the body (or) on the point where all the medians or diagonals of the body are intersecting. • Example : In the case where the position of Centre of gravity is formed in the Centre of the object. Rod , Circular Disc , Circular ring , Square , Rectangle , Rhombus , Parallelogram , Triangle , Sphere , Cube , Cuboid , etc. Centre of gravity at : Point of intersection of diagonals – Square,Rectangle,Rhombus,parallelogram Geometric Centre – Sphere,cube,cuboid

8. (a)Line (b)Rod (c)circle (d)annular ring (e)triangle(f)rectangle (g)kite (h)sphere (i)cone(1/4) (j)cone(1/3) (k)cuboid

9. Where is the position of Centre of gravity of  an irregular shaped lamina??? • Take a cardboard and cut it in an irregular shape and there you obtain an irregular shape lamina. • Make 3 holes namely P,Q,R • Then suspend the lamina on a retort stand from the point P. • Hang a plumbline from the point P and mark the place where the plumbline comes to rest as PI and draw I line between them. Do the same with the rest of the two holes.  • We observe that all the lines meet at a point. That is the Centre of gravity.

11. What do you mean by Stability of bodies??? • Stability refers to the ability of abodyto restore to its original staticequilibrium, after it has been slightly displaced. A body in equilibrium experiences neither linear acceleration nor turning effect and, unless disturbed by an outside force, will continue in that condition indefinitely                                                            (OR) •  The property of a body that causes it when disturbed from a condition of equilibrium or steady motion to develop forces or moments that restore the original condition.

12. Conditions for stability of a body • The Centre of gravity should be as low as possible. Bodies with heavy base are stable. • Motorists should not keep too much luggage on the top of their cars as this raises the center of gravity and makes the cart more prone to toppling over. • Cargo ships are heavily loaded at the base which lowers the center of gravity. • Overloaded lorries and hay carts are not allowed up and down mountain slopes their center of gravity is Rays because of the Lord and they can topple over on mountain roads.

13. 2) The base of the body should be as broad as possible so that  the vertical line(the line of action)falls within the base. Pedestal fan table lamp bunsen burner , etc. are having broad bases which prevent their toppling over A person standing with his feet wide apart has larger area of support and is more stable than a man standing in one foot.

14. What is Equilibrium and its states??? • Equilibrium is defined as a state of balance or a stable situation where opposing forces cancel each other out and where no changes are occurring. • There are 3 states of equilibrium - • Stable equilibrium • Unstable equilibrium • Neutral equilibrium

15. STABLE EQUILIBRIUM • A equilibrium is said to be stable if small, externally induced displacements from that state produce forces that tend to oppose the displacement and return the body to its original equilibrium.

16. UNSTABLE EQUILIBRIUM •  An equilibrium is said to be unstable if the least departures produce forces or torques that tend to increase the displacement.

17. NEUTRAL EQUILIBRIAM •  An equilibrium is said to be neutral if small, externally induced displacements from that state does not produce any unbalanced forces or torques that tend to oppose or aggravate the displacement and the body remains in its new equilibrium.