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# Newton s Laws of Motion

Posted by on Jun 1, 2018 in Physics | 1 comment

Newton s Laws of Motion major on forces that act on objects that are on the earth’s surface and beyond.

# Newton s Laws of Motion

The first law in Newton s Laws of Motion

The law in Newton s Laws of Motion states that: – a body tends to remain at rest or in uniform motion in a straight line (with constant velocity) unless acted upon by a resultant force. The tendency of a body to continue in its initial state of motion (a state of rest or a state of uniform motion in a straight line) is called inertia in Newton s Laws of Motion.

The second law in Newton s Laws of Motion

The law in Newton s Laws of Motion states that: – if a net force acts on a body, it will cause an acceleration of that body. That acceleration in the direction of the net force and its magnitude is proportional to the magnitude of the net force and inversely proportional to the mass of the body i.e. a α F/m, so that F = kma. This vector equation is a relation between vector quantities F and a and thus applies to the x, y and z planes of the Cartesian plane in Newton s Laws of Motion.

The third law in Newton s Laws of Motion

The law in Newton s Laws of Motion states that: – action and reaction forces are always equal and opposite i.e. when a body in Newton’s Laws of Motion exerts a force on another, the second exerts an equal, oppositely directed force on the first. Examples include when pushing on a car, the car pushes back against your hand. When a weight is supported by a rope, the rope pulls down on the hand.

A book resting on a table pushes down on the table, and the table in turn pushes up against the book. The earth pulls on the moon holding it in a nearly circular orbit and the moon pulls on the earth causes tides.

The third law in Newton s Laws of Motion however differs from the first and the second in that; whereas the first and second laws in Newton’s Laws of Motion are concerned with the behaviors of a single body, the third law in Newton’s Laws of Motion is concerned with two separate bodies. The inherent symmetry of the action-reaction couple precludes identifying one as action and other as reaction in Newton’s Laws of Motion.

## Collisions and Linear Momentum according to Newton s Laws of Motion

Linear momentum (L) is defined as the product of the object’s mass (m) and its velocity (v) and is a vector quantity. The SI unit of linear momentum is kgms-1, which in Newton’s Laws of Motion can be called the Newton-second (Ns). From the second law in Newton s Laws of Motion (F=ma), if no external force acts on an object, then;

F=ma=m {(v-u)/t} =∆L/t=0→L is a constant. Thus it momentum is conserved. This is the principle of conservation of linear momentum in Newton s Laws of Motion.

It is useful in solving problems involving collisions between bodies. The product of the force and the time in Newton’s Laws of Motion is called impulse, denoted by the letter I.

Impulse (I)=Ft=(mv-mu)=change in momentum. The SI unit of impulse is the same as that of momentum i.e. Newton-second or kgms-1.

Collision: – a collision in Newton s Laws of Motion is any strong interaction between bodies that lasts a relatively short time. Examples include automobile accidents, neutrons hitting atomic nuclei in a nuclear reactor, balls colliding; the impact of a meteor on the surface of the earth, a close encounter of a spacecraft with the planet etc. in all collisions in Newton’s Laws of Motion, momentum is conserved. The total energy is also conserved. However, kinetic energy might not be conserved since it might be converted to other forms of energy like sound, heat or work during plastic deformation. There are two main types of collisions in Newton’s Laws of Motion;

Elastic collisions in Newton s Laws of Motion

For elastic collisions in Newton s Laws of Motion, both momentum and kinetic energy (K.E) are conserved.

a) Before collision                                            b) after collision

Assuming that before collision the velocities of ma and mb are ua and ub respectively, and those of ma and mb after collision are va and vb;

maua + mbub = mava +mbvb (conservation of linear momentum)

½maua2 + ½mbub2 = ½mava2 + ½mbvb2 (conservation of kinetic energy).

Inelastic collisions in Newton s Laws of Motion

For inelastic collisions in Newton s Laws of Motion, momentum is conserved but kinetic energy is not conserved. Thus

maua + mbub = mava +mbvb

If the colliding bodies stick together, the collision is totally inelastic and hence we have

maua + mbub = (ma + mb)V where V is the common velocity in Newton s Laws of Motion.

### Conclusion on Newton s Laws of Motion

Collisions in Newton s Laws of Motion can be special. When the mass of the two objects is equal, or the objects collide at an angle (obliquely), the cases are said to be special in Newton s Laws of Motion.

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