Derive the equation F = ma.

1.	Derive the equation F = ma.
Answer» Consider a body of mass ‘m’ moving with a velocity ‘u’. Let a constant force ‘F’ applied on a body changes its velocity to V in ‘t’ seconds. Initial momentum of the body = mass × initial velocity = m u Final momentum = mass × Final velocity = m v Change of momentum in ‘t’ seconds = mv – mu. = \(\frac {mv-mu}{t}\)= m \((\frac{v-u}{t})\) ∴ α = ma ∵ \((\frac{v-u}{t})\) = a, acceleration. According to Newton’s second law, the rate of change of momentum is directly proportional to the applied force or vice versa. i. e. Force a rate of change of momentum F α ma F = kma Where ‘k’ is a proportionality constant. In SI system k = 1. ∴ F = ma.

Answer»

Consider a body of mass ‘m’ moving with a velocity ‘u’. Let a constant force ‘F’ applied on a body changes its velocity to V in ‘t’ seconds.

Initial momentum of the body = mass × initial velocity = m u

Final momentum = mass × Final velocity = m v

Change of momentum in ‘t’ seconds = mv – mu.

= \(\frac {mv-mu}{t}\)= m \((\frac{v-u}{t})\)

∴ α = ma

∵ \((\frac{v-u}{t})\) = a, acceleration.

According to Newton’s second law, the rate of change of momentum is directly proportional to the applied force or vice versa.

i. e. Force a rate of change of momentum

F α ma

F = kma

Where ‘k’ is a proportionality constant.

In SI system k = 1.

∴ F = ma.

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