Question

Derive a mathematical expression for force.

Answer 1

Answer:

According to the Newton’s 2nd law of motion, the rate of change of linear momentum of a body is directly proportional to the external force applied and this change takes place in the direction of force.

Thus, larger the force more the change in linear momentum.

Let us take a body of mass ‘m’ moving with velocity v.

The linear momentum p of a body is given by:

P = mv

Using Newton’s 2nd law of motion, we get

(Since force is directly proportional to rate of change of momnetum)

F α dp/dt

F = k dp/dt

(Where k is constant of proportionality)

F = k d(mv)/dt

F = k m dv/dt

F = k ma

(Since rate of change of velocity is acceleration)

Experimentally k =1

Which gives, F = ma

This is required relation.

Unit of force is N.

1 newton = 1 kg × 1 m/s²

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