Force

Chapter 2

Force

Rest

          A body is said to be at rest if its position does not change with time with respect to an observer or a reference point.

Motion

A body is said to be in motion if its position changes with time with respect to an observer or a reference point.

Force

          Force is that push or pull on a body that change or tends to change its state of rest or uniform motion in a straight line.

Balanced forces

          When a number of forces acting on a body do not change its state of rest or uniform motion in a straight line, the forces are said to be balanced forces.

Unbalanced forces

          When a number of forces acting on a body changes its state of rest or uniform motion in a straight line, the forces are said to be unbalanced forces.

Speed

          Speed is defined as the distance travelled per unit time.

          Mathematically,

                   Speed(v) = distance travelled(d) / time taken (t)

          It is scalar quantity and its SI unit is m/s.

Uniform speed

          If a body travels an equal distance in equal interval of time, then the body is said to have uniform speed.

Non-uniform speed

If a body travels an unequal distance in equal interval of time, then the body is said to have non-uniform speed.

Average speed

          The average speed is defined as the total distance travelled by the body per unit time taken by it.

          Mathematically,

                   Average speed = total distance travelled(d) / total time taken(t)

Velocity

          Velocity is defined as displacement per unit time.

          Mathematically,

                   Velocity(v) = displacement(s) / time taken(t)

          It is vector quantity and its SI unit is m/s.

Difference between speed and velocity

S.N.	Speed	S.N.	Velocity
1.	It is the distance travelled per unit time.	1.	It is the displacement per unit time.
2.	It is scalar quantity.	2.	It is vector quantity.
3.	It is always positive.	3.	It can be positive or negative.

Uniform velocity

          A body is said to move with uniform velocity if the body covers an equal distance in equal interval of time on a straight line. It is called constant velocity.

Non-uniform velocity

          A body is said to move with non-uniform velocity if the body covers unequal distances in equal intervals of time on straight line.

Average velocity

          Average velocity is as the total displacement made by a body per unit time.

          Mathematically,

                   Average velocity(Av) = total displacement(s) / time taken(t)

Change of velocity can be done by:

1.    Changing the speed of a body and keeping the direction same.

2.    Changing the direction of motion by keeping the speed constant.

3.    Changing both the speed and direction of the body.

Acceleration

          Acceleration is defined as change in velocity per unit time.

          Mathematically,

                   Acceleration = change in velocity / time taken

                   i.e.    a        =        (v – u) / t

Retardation

          The decrease in velocity per unit time or negative acceleration is known as retardation.

Equations of motion of uniform acceleration

a.    Relation between u, v, a and t.

From the definition of acceleration, we have

Acceleration = change in velocity / time taken

            or,  a  = (v – u) / t

            or,  at = v – u      

              ∴ v  = u + at

This is the first equation of motion.

b.    Relation between s, u, v and t.

From the definition of average velocity,

Av = (u + v)/2 ………(i)

Av = s / t ……………..(ii)

Solving equations (i) and (ii),

Both equations are equal, we have,

or, (u + v)/2 = s / t

or, s = {(u + v)/2}*t

or, s = {(u + u + at)/2}*t   [∵ v = u + at]

or, s = {(2u + at)/2}*t

or, s = (2ut + at²)/2

or, s = (2ut/2) + (at²/2)

∴ s = ut + 1/2at² 

Gravitational Force

                Gravitational Force is defined as the mutual force of attraction between any two objects or bodies in the universe.

Newton’s universal law of gravitation

                Newton’s universal law of gravitation states, “every object in the universe attracts each other with a force called gravitation which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.”  

Verification of Newton’s law of gravitation

                F ∝ m₁ × m₂ ………………(i) (keeping the distance constant)

                F ∝ 1/d² ……………………(ii) (keeping the masses constant)

                Combining equations (i) and (ii), we have,

                F ∝ ( m₁ × m_{2) /} d²

 or,         F = G ( m₁ × m_{2) /} d²  ………………(iii) (where G is constant known as universal gravitational constant)

Universal Gravitational Constant

                Universal Gravitational Constant is defined as the gravitational force between two bodies of unit mass each separated by unit distance from their centers.

                Its SI unit is Nm²kg^-2 and its value is 6.67 × 10^-11 Nm²kg^-2.

Consequences of gravitational force

1. Tides in sea and oceans are occurred due to the gravitational force of the sun and the moon.
2. Objects falls towards the center of the earth and water flows downwards due to the presence of gravitational force.
3. The existence of solar system and revolution of planets and satellites round the sun become possible due to gravitational force.
4. The presence of atmosphere on the surface of the earth is due to the gravitational force.
5. The gravitational force of earth keeps us firmly on the surface of the earth.
6. Velocity of the body changes due to the gravitational force of the earth when it falls down and thrown up.

Special feature of gravitational force

                The gravitational force between light bodies is extremely small and hence such smaller force is not felt in practice. However, it becomes notable in case of larger bodies.