**Force and laws of motion** **notes** – **Chapter 9**

**Force**

Any action which causes pull, hit or push on a body is called force.

**Many effect of force are as given below:**

(i) A force can move a stationary body.

(ii) A force can stop a moving body.

(iii) A force can change the direction and speed of a moving body.

(iv) A force can change the shape and size of a body.

**Balanced and Unbalanced forces**

**Balanced forces**

When the net effect produced by a number of forces acting on a body is zero, then the forces are said to be balanced forces.

**Unbalanced forces**

When the net effect produced by a number of forces acting on a body is non-zero, then the forces are said to be unbalanced forces.

**Newton’s Law of Motion**

**Newton’s first law of motion**

It states that an object will continue to remain in its state of rest or in a uniform motion along a straight line or push unless and external forces acts on it.

**Inertia and mass**

The unwillingness (or inability) of an object to change is state of rest of of uniform motion along a straight line is called inertia of the object.

Inertia of an object measured by its mass. Inertia is directly proportional to the mass. It means that inertia increases with increase in mass and decreases with decrease in mass. A heavy object will have more inertia than lighter one.

**Momentum**

It is defined as the product of mass and velocity of the body.

p = mv

The SI unit of momentum is kg-m/s.

**Newton’s second law of motion**

The second law of motion states that the rate of change of momentum of an object is proportional to the applied external force and takes place in the direction in which external force acts.

**Mathematical formulation of second law of motion**

If a body of mass m moving at initial velocity u accelerates uniformly with an acceleration a for time t, so that its final velocity changes to v, then

Initial momentum, p1 = mu

Final momentum, p2 = mv

Therefore Change in momentum = p2 – p1 = mv – mu

= m(v – u)

According to the second law of motion,

force, F ∞ change in momentum/time

→ F ∞ p2 – p1/t → F ∞ m (v – u)/ t

→ F∞ma. [Because v-u/t = a]

Therefore F = kma

The quantity k is a constant of proportionality.

One unit of force is defined as the amount that produces an acceleration of 1m/s² on an object of 1kg mass.

i.e. 1 unit of force = k × 1kg × 1m/s²

→ k= 1

Thus, the force can be written as

F = ma

**Impulse**

Impulse is defined as the product of force and a small time in which force act.

Impulse, I = Ft = p2 – p1

**Newton’s third law of motion**

The third law of motion states that, whenever one object exerts a force on another object, then the second object exerts an equal and opposite force on the first object.

**Law of conservation of momentum**

Consider a system of objects of masses m_{A} and m_{B} moving with initial velocities u_{A} and u_{B} respectively, (where, u_{A} > u_{B}) in the same direction. After collision, the bodies move with velocities v_{A} and v_{B}, respectively. The collision lasts for time t.

m_{A}u_{A} + m_{B}u_{B} = m_{A}v_{A} + m_{B}v_{B}

**Try To Solve These Questions**

_{Q1. What is First Law of Motion?}

_{Q2. Define Second law of Motion?}

_{Q3. What is Third Law of Motion?}