Question

write mathematical expression of Newton's second law of motion ​

Answer 1

Answer:

Newton's second law of motion states the rate of change of momentum of a body which is directly proportional to the applied force and in the direction in which the force acts.

Mathematical expression of Newton’s Second Law of Motion:

Let mass of an moving object be m.

Let is initial velocity be u and final velocity be v.

We know that momentum (p) = Mass × velocity

Therefore,

Initial momentum of object = m×u

And Final momentum of the object = m×v

Therefore, change in momentum =

final momentum-initial momentum

=mv – mu

Where k is the proportionality constant

Now, 1 unit force is defined as the force applied on an object of mass 1kg to produce the acceleration of 1m/s2.

Thus, 1 unit of force = k ×1kg ×1m/s2

⟹       k = 1

By putting the value of k=1 in equation (ii), we get:

    F = ma

i.e., Force = Mass × Acceleration

The unit of mass = kg and The unit of acceleration = m/s2

If force, mass and acceleration is taken as 1 unit.

Therefore,

1 Newton (N) = 1kg x 1m/s2

Thus, Newton (N) = kg m/s2

Thus, one unit of force is defined as the amount that produces an acceleration of 1 m/s2 in an object of mass 1 kg.

Answer 2

Newton's second law of motion ​can be stated as follows:

The rate of change of momentum of a body is directly proportional to the applied force and this change takes place in the direction of the applied force.

• Linear momentum of a body is the product of the mass and the velocity of the body.
• It is given by the following formula.

        $p = m * v$

• Here, p is the linear momentum of the body, m is the mass of the body and a is the acceleration.
• A heavier body has a larger linear momentum than a lighter body moving with the same velocity.
• Newton's second law provides a quantitative definition of force by implying that the rate of change of momentum of a body is directly proportional to the applied force.

        $F \alpha \frac{dp}{dt}$