Newton’s Laws of Motion

Newton’s Laws of Motion

→ Newton studied the ideas of Galileo and gave the three laws of motion. These laws are known as Newton’s laws of motion.

Newton’s First Law of Motion (Law of Inertia)

→ Any object remains in the state of rest or in uniform motion along a straight line, until it is compelled to change the state by applying external force.

Explanation: If any object is in the state of rest, then it will remain in rest until a external force is applied to change its state. Similarly, an object will remain in motion until any external force is applied over it to change its state.

This means all objects resist to in changing their state. The state of any object can be changed by applying external forces only, this property is called inertia.

• Newton’s First Law of Motion in Everyday Life

(i) A person standing in a bus falls backward when bus starts moving suddenly.

→ This happens because the person and bus both are in rest while bus is not moving, but as the bus starts moving, the legs of the person start moving along with bus but rest portion of his body has the tendency to remain in rest. Because of this, the person falls backward; if he is not alert.

(ii) A person standing in a moving bus falls forward if driver applies brakes suddenly.

→ This happens because when bus is moving, the person standing in it is also in motion along with bus. But when driver applies brakes the speed of bus decreases suddenly or bus comes in the state of rest suddenly, in this condition the legs of the person which are in contact with the bus come in rest while the rest part of his body have the tendency to remain in motion. Because of this person falls forward if he is not alert.

(iii) Before hanging the wet clothes over laundry line, usually many jerks are given to the clothes to get them dried quickly. Because of jerks, droplets of water from the pores of the cloth falls on the ground and reduced amount of water in clothes dries them quickly.

→ This happens because when suddenly clothes are made in motion by giving jerks, the water droplets in it have the tendency to remain in rest and they are separated from clothes and fall on the ground.

(iv) When the pile of coin on the carom-board is hit by a striker, coin only at the bottom moves away leaving rest of the pile of coin at same place.

→ This happens because when the pile is struck with a striker, the coin at the bottom comes in motion while rest of the coin in the pile has the tendency to remain in the rest and they vertically falls the carom-board and remain at same place.

Statement of Second Law of Motion

→ Rate of change of momentum of an object is proportional to applied unbalanced force in the direction of force.

Mathematical expression

Suppose, Mass of an object = m kg

Initial velocity of an object = u m/s

Final velocity of an object = v m/s

∴ Initial momentum, p₁ = mu

Final momentum, p₂ = mv

∴ Change in momentum = Final momentum – Initial momentum

= mv – mu

= m(v – u)

∴ Rate of change of momentum = Change in momentum/Time taken

= m(v-u)/t

•  According to 2nd law, this rate of change is momentum is directly proportional to force.

We know that, a = (v-u)/t (From 1st equation of motion)

∴ F = kma

where, k is a constant. Its value can be assumed as 1.

∴ F = 1 × m × a = ma

• SI unit = kg m/s² or Newton

1 Newton: When an acceleration of 1 m/s² is seen in a body of mass 1 kg, then the

force applied on the body is said to be 1 Newton.

Proof of Newton’s First Law of Motion from Second Law

→ First law states that if external force F = 0, then a moving body keeps moving with the same velocity, or a body at rest continues to be at rest.

∴ F = 0

We know, F = m(v-u)/t

(i) A body is moving with initial velocity u then,

m(v-u)/t = 0 ⇒ v – u = 0

∴ v = u

Thus, final velocity is also same.

(ii) A body is at rest i.e., u = 0

Therefore, from above u = v = 0

So, the body will continue to be at rest.

Third Law of Motion

→ For every action there is an equal an opposite reaction.

Applications

(i) Walking is enabled by 3rd law.

(ii) A boat moves back when we deboard it.

(iii) A gun recoils.

(iv) Rowing of a boat.