Newton’s laws of motion

Newton’s laws of motion

Newton’s laws of motion: Before we discuss Newton’s laws of motion, note that forces are the only thing that cause the motion of a body.

Forces: it can be defined as agent that can change or tend to change the state of rest or uniform motion of a body in a straight line. There two type of force- contact force and field force.

Contact forces: these are force that must be in contact with the body they act on. Example is tension and reaction forces, frictional force and force of pull or push

Field forces: these are forces which do not require contact before they act on anybody or objects. Examples of such forces are gravitational forces, electrical forces, and magnetic force. The effects of these forces are felt at distance or in a field

Filed: it is a region or area, where effects of force are felt. Examples of fields are Electric field, gravitational field and magnetic field.

Newton’s laws of motion (first)

The Newton’s first law of motion state that a body will continue in its present state of rest or uniform motion, unless is acted upon by force. The tendency of a body to remain in its state of rest or uniform motion is called inertia.  Therefore Newton’s first law of motion can be called law of inertia.

The tendency of a body to continue in it state of rest or continue in its uniform motion is observed when a  moving vehicle is suddenly brought to rest by the application of brakes, the passengers  are jerked forward , as they tend to continue in their straight line motion. The passengers in the front may hit the windscreen.  This is why it is advisable to use a safety belt in cars.

It is important to note that a body which is already in uniform motion in a straight line , need no force to keep on moving, provided no external  opposing or accelerating force. For example if a body is thrown up to the air, it would have continued in its uniform motion for ever, if not for air resistance and force of gravity that pull it down toward the Earth.

Before we go further in discussion of Newton’s laws of motion, is good we discuss momentum

Momentum which is important property of a moving object, explains its tendency of a body to continue moving in a straight line.

Momentum of a body is defined as the products of the mass of the body and its velocity and is given as:

Momentum =MV where M = mass, and v = velocity. The units of momentum is kgms-1

Law of conservation of momentum

Momentum of small and big mass in motion

The bullet which has a mass of 0.01kg, moving with a high velocity of 10000m/s and a ball of 100kg moving with a small speed of 1m/s has the same momentum with the bullet.  Note that the high the momentum of a bullet the more deadly it is , and also more brakes, are required  to stop a heavy lorry than a light car moving with the same speed.

Newton’s laws of motion (Second)

The Newton’s second law of motion state that, the rate of change of momentum of a body is directly proportional to the applied force and takes place in direction in which force is applied. That is:

F\propto \frac { Change\quad in\quad momentum }{ time }

Assuming that  a force F, acts on a body of mass, m, for time t, and causes it to change its velocity from u to v, then Newton’s second law of motion can be written as:

F\propto \frac { Mv-Mu }{ t } ,\quad that\quad is\quad F\propto \frac { M(v-u) }{ t } ,\quad but\quad a=\frac { v-u }{ t }

therefore\quad F\propto Ma,\quad thus\quad F=kMa,\quad where\quad k\quad =\quad constant

If m=1 , a =1 and F=1, then k =1, therefore we have

F =ma, this equation is called equation of dynamics

Deduction from Newton’s  laws of motion (second)

From the second law of motion, Impulse which is the product of a large force and a very short small time t, during which it act, can be deduced.

From\quad F=\frac { M(v-u) }{ t } ,\quad which\quad implies\quad that\quad Ft=M(v-u)

So the quantity Ft is called impulse , the unit of impule is Ns (Newton second).  From the deduced formula of impulse, it can also be defined as change in momentum , that is

Ft = M(v-u) = change in momentum.

Newton’s laws of motion (Third)

The Newton third law of motion, state that to every action there is equal and opposite reaction.

For instance , if we place an object on a table the reaction of the table on the object ( that is vertical force exerted on the object by the table) is equal and opposite to the action of the object on the table ( that is the weight of the object bearing downward on the table.

Likewise if a moving car  A hit a stationary car B, the force exerted on B by A will be the same as the action of B on A, that is while both cars are damaged

More so, is when a bullet  shot out of the gun, the person firing it experience the backward recoil force of the gun (a reaction), which is equal to the repulsive force (action) acting on the bullet.

Since the force is proportional to change in momentum, therefore the momentum of the bullet is equal and opposite to the momentum of the gun. So the velocity of recoiling gun and the velocity of bullet is related as

V=\frac { -vm }{ M }

Where M, V and m,v are velocity and mass of gun and bullet respectively

 

Newton’s third law of motion has very useful application, in operating of jet aero-planes and rocket. The application is based on the fact that the velocity and mass per second of  a large mass of hot gases coming out from the nuzzle behind the jet or rocket are so high, so large momentum is imparted on the stream of gases.  Therefore an equal and opposite momentum is imparted to the rocket or aero -plane which undergoes forward thrust.

Examples  on Newton’s laws of motion

  1. A body of mass 2kg undergoes a constant horizontal acceleration of 10ms-2.(a) Calculate the resultant horizontal force acting on the body and, (b) what will be the resultant force on the body when it moves with uniform velocity of 10ms-1

Solution,

Using    F = ma where m = mass =2kg, a =10m/s2 , therefore F = 2 x 10 = 10N

So F=10N

For (b) If object moves with uniform velocity, it means it was not accelerating, ie is

Acceleration a =0,   therefore F = m x o = 0, so F = 0

  1. A car of mass 600kg, moving with a forward acceleration of 5m/s2 is acted upon by a constant resistive force of 1000N. Calculate the force exerted from the engine to maintain this forward acceleration.

        Solution,

Using      F-1000N=ma,

Where F =force exerted by the engine to maintain its acceleration, 1000N = resistive force

So  F – 1000 = 600 x 5 , F=  3000 + 1000 =4000N

Therefore the force exerted by engine to maintain it acceleration = 4000N

  1. A body of mass 5kg moving with a speed of 30m/s, is suddenly hit by another body moving in the same direction , thereby changing the speed of the former body to 60m/s. what is the impulse received by the first body.

Solution,

using

Impulse = change in momentum = m(v-u) = 5(60-30) = 5 x 30 = 150Ns therefore

Impulse =150Ns

  1. A body of mass 5kg is to be given an acceleration of 20m/s2. Calculate the force required, when the acceleration is vertically upwards. Take g = 10m/s2

       Solution,

let F = force required for the vertical acceleration, W = weight of the body                               downward

So using F –w = maF-mg = ma , therefore

          F = mg +ma = (10 x5) + (5 x 20) = 50 + 100 = 150N

You can as well, read law of  conservation of momentum , as derived from Newton’s law of motion

 

 

 

 

 

 

 

 

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