Newton's Laws of Motoin

In the year Galileo died (1642) a baby boy was born in England who grew up to explain all types of motion known at the time. As he had a brilliant knowledge of mathematics he was able to explain the observed facts in the form of precise laws leading to simple equations.

**Fig. 1 Sir Isaac Newton 1642 - 1727. UK. **

This was no other person than Sir Isaac Newton, who stated the **“The Law of Universal Gravity**” and the **3 Laws of Motion** which have stood the test of time for three centuries.

First Law

**"A body will remain at rest or move at the same velocity unless an unbalanced force is acting on it."**

In his first Law he explains that matter is very lazy to change the state of motion. He called this property** inertia.**This law is explained here in three sentences.

1. If a body is still , it will remain so , until an unbalanced force acts on it.

2. If a body is moving , it will maintain the velocity (without the use of a force) until an unbalanced force acts on it..

3. Balanced forces may act on a still body or on a moving body, without causing an acceleration.

Let us take an example for each of these.

1. A book on your table will remain there until a force acts on it.

2. When a driver jams the brakes, the passengers get thrown forward.

3. When the forces on a plane are balanced , as in the diagram here, it travels at the same velocity, without changing the height.

**Fig.2 Aeroplane cruising with the forces balanced.**

Drag = Thrust

and Weight = Lift.

Click "The cat sits on a mat" in our web site and conduct the experiment given there. It is connected with "inertia"

Second Law

Newton;s Second Law may be stated in two different ways.

**Method 1 **

,**“Acceleration is directly proportional to force while inversely proportional to mass”**

Mathematically we can express this as:

Force = Mass X Acceleration

**F = ma.**

**Method 2**

Here we use a concept called **momentum.**

Momentum is the product of Mass and Velocity of an object.

Momentum = Mass X Velocity

Taking p as momentum:-

**P = MV **

** Force = (P**_{2} - P_{1}) / time

*"This, rate of change in Momentum is directly proportional to Forc* ** **

**An Application = A Unit for Force.**

When we take mass in kilograms and the velocity in meters per second, we get the momentum in kgXms^{-1}. (kg.ms^{-1}) Then the rate of momentum, which is equal to force, becomes kg X ms^{-2}

The force that can bring about this change is taken as the unit of force. This unit has been named as Newton to honour the scientist who stated the laws of motion, which helped to define this.

*What is a newton; the unit of measuring force?*

**Definition 1**

**One newton is the force that can produce an acceleration of 1 m.s**^{-2} on a mass of 1 kg.

**Definition 2****One newton is the force that can produce a change in momentum of 1 kg.m/s in one second.**

*What is Impulse?*

the product of the average value of a force and the time This is equal to change in momentum.

Impulse = Force x duration.

**Imp. = F**_{av}. x t_{2} - t_{1}.

Third Law

*"*When a body ‘A’ exerts a force on another body ‘B’, the latter will also exert a reaction force which will be equal and opposite."

Have you ever jumped out of a boat. You may have at least seen that as a person jumps out of a floating object, that object gets a kick. It is impossible for anyone to jump out without kicking the boat in this manner.

**Fig. 3 Jumping diver has to give a kick back..****Fig.4. Man pulls the tree and tree pulls the man.** It should be clear to you now, when ever there is a force in a particular direction, there has to be a force in the opposite direction too. The first force we can recognize may be called the ‘action’, then the other becomes the ‘reaction’.

**Action** | **Reaction** |

i.A weight on a table | Reaction from table ( Support force) |

ii.Pulling a bucket of water with a rope. | Earth pulling the bucket of water down. |

iii Earth pulls astronaut | .................................................. |

** ***Can you add a few more examples to this?* **The Third Law may be stated as follows:**

" Every action has an equal and opposite reaction."

**Applications of the Law**

The law is often applied to work out problems of mass and acceleration in jets and rockets., These work on a principle similar to what happens in Fig……..When burnt out gases escape , the rocket goes up. According to Newton’s law the two forces are equal.

**1.0**

A force of 1,000. N . acts on an object of 10 kg. Mass. Find the following:

i. Acceleration.

ii. If the body started from a velocity of 10m/s, the final velocity after 3 seconds.

iii. The momentum after 3 seconds.

iv. Change in momentum.

v. Rate of change in momentum.

**2.0**

A ball of 0.5 kg. mass, moving at a velocity of 30m/s was held by a fielder and brought to rest in 0.2 seconds.

Find the following:

i. First momentum of the ball.

ii. Final momentum of the ball.

iii. Change in momentum.

iv. Impulse produced.

v. The force on the hand.

**3.0**

A car traveling at 40m/s. crashed on to a pillar and got dented as follows:

Length of car after crash = 2.0m

Original length off the car 2.5 m

Length after crash 2.0 m

The distance the pillar moved. = 0.25m

Mass of car & driver = 1200kg.

Find the following.

i. Total stopping distance.

ii. The average velocity of stopping.

iii. Time taken to stop.

iv. Change in momentum of car.

v. Force on the pillar.

**4.0**

Two toy vehicles are connected to an elastic tape. and pulled apart until the distance between them becomes 2m..

If the spring balance attached indicate a force of 500N find the following:;

Mass of A 0.25kg. Mass of B is 1.0kg

i. Are the forces on the two objects equal or unequal?

ii. Which one would show a higher acceleration? A or B.?

iii. Acceleration on A.

iv. Acceleration on B

v. Distance A travels

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