by on September 17, 2020
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Momentum

Momentum of a body is defined as the product of its mass and the velocity of the body.

Mathematically,

Momentum = mass    x   velocity =mv

The unit of momentum is  Kgm

Example

What is the momentum of an object with mass 0.01kg and another object of mass 100kg, if they are moving with velocity of  10000m and 1m respectively ?

Solution

Momentum = mv =0.01 x 10000= 100 Kgm

For the second object,

Momentum = 100 x 1 = 100 Kgm

These two objects have the same momentum.

When these two object collide with a stationary body, they impacted the same force.

Newton's Second Law of Motion

Newton’s second law state that the rate of change of momentum of a body is directly proportional to applied force and is in the direction in which the force acts.

This law is also called the law of Acceleration

The acceleration produced by a net force on an object is directly proportional to the net force in the same direction and inversely proportional to the mass of the object.

 

  

If a force F  is applied on a body of mass m for a time t and this changes its velocity from u to v .

Then newton's second states that;

      

  

   

 

 

 Where k is the constant of proportionality, and is defined as the resultant force applied when a body of mass 1kg is moved with an acceleration of 1m in the direction of the force. When k=1

    

  

Where F is the resultant force in Newton,

m is the mass in kg

 a is the acceleration in   m

This is the fundamental equation of Dynamics.

Example

A body moves with uniform velocity of 20m for 10s. what is the resultant  force applied on the body ?

Solution

F=ma     =  

The resultant force on the body is zero.

If this body has a mass 30kg and the velocity changes from 20m  in 10s. what is the resultant force applied ?

F=ma

Example

The engine of a jet exact a force of 4500N . If this jet has a mass of 1000kg and  moved with an acceleration of 4 . what is the value of the frictional force from air and gravity combined against the motion of the jet ?

Let the resultant effect of gravitational force and air resistance be f

     

,     

4500-4000=f   

f=500N

 

The impulse of a force

The products of a force and the time it takes the force to act is called impulse of a force.

From the newton’s second law,

 

 F, and is the change in the momentum   when the velocity changes from u to v as a result of the force F  .The unit is Newton seconds Ns.

EXAMPLE

 A force is applied on a body of mass 30kg at rest. if this force changes the velocity to  2, what is the impulse of the force ?

v=2, u=0, m=30

A force of 40N acts on an object for 30s . what is the change in momentum of the object ? if the object has a mass of 200kg and final velocity of 10. What is the initial velocity of the object ?

 

 

 

  

 

 

 

 

Read more about PHYSICS for High Schools

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