- Force is a push or a pull acting on an object which tends to change or change its state of rest or of uniform motion, or the direction of motion, or even the shape and size of the object.
- From Newton's Second Law of Motion, we can derive the formula of force.
- Newton's Second Law states "The rate of change of momentum of a body is directly proportional to the applied unbalanced force in the direction of force.
- Let the assume a body of mass m with an initial velocity u. Suppose a force F acts on the body for time t. Consider the final velocity as v.
- Initial momentum of the body (pi) = mu
- Final momentum of the body (pf) = mv
- Therefore, Change in momentum = pf-pi = mv-mu = m(v-u)
- Rate of change of momentum
[tex] = \frac{Change \: \: \: \: in \: \: \: \: momentum
}{Time \: \: \: \: taken} \\ = \frac{m(v - u)}{t} \: \: \: ...(1)[/tex]
- We know, v=u+ at (equation of motion)
- [tex] = > a = \frac{v - u}{t} ...(2)[/tex]
- Putting the value of (2) in (1), we get
- Rate of change in momentum = ma
- According to Newton's second law of motion,
- F ∝ rate of change of momentum
- F ∝ m × a
- The relation F ∝ m × a can be turned into an equation by putting in a constant k. Then
- F = k × m × a ...(3) [where k is a constant of proportionality]
- The unit of force is chosen in such a manner that the constant of proportionality becomes one. The Sl unit of force is newton (N). We define one newton as that force which when acting on a mass of 1 kg produces in it an acceleration of 1 m/s² in its own direction, i.e. when m = 1 kg, a = 1 m/s^2, then F = 1N
- 1 N=1 kg m/s^ 2
- Let us substitute these values in equation (3), we get
- 1N = k × 1 kg × 1 m/s^2
k = 1 [Newton is equivalent to kg m/s²]
- Therefore, F = ma [For k = 1]
- So, we can find out force by multiplying the mass of the object with its acceleration.
Hope you could get an idea from here.
Doubt clarification - use comment section.
