- Books Name
- Science Made Easy Science Book
- Publication
- Science Made Easy
- Course
- CBSE Class 9
- Subject
- Science
Statement of Second Law of Motion
→ Rate of change of momentum of an object is proportional to applied unbalanced force in the direction of force.
Mathematical expression
Suppose, Mass of an object = m kg
Initial velocity of an object = u m/s
Final velocity of an object = v m/s
∴ Initial momentum, p1 = mu
Final momentum, p2 = mv
∴ Change in momentum = Final momentum – Initial momentum
= mv – mu
= m(v – u)
∴ Rate of change of momentum = Change in momentum/Time taken
= m(v-u)/t
• According to 2nd law, this rate of change is momentum is directly proportional to force.
We know that, a = (v-u)/t (From 1st equation of motion)
∴ F = kma
where, k is a constant. Its value can be assumed as 1.
∴ F = 1 × m × a = ma
• SI unit = kg m/s2 or Newton
1 Newton: When an acceleration of 1 m/s2 is seen in a body of mass 1 kg, then the
force applied on the body is said to be 1 Newton.
Proof of Newton’s First Law of Motion from Second Law
→ First law states that if external force F = 0, then a moving body keeps moving with the same velocity, or a body at rest continues to be at rest.
∴ F = 0
We know, F = m(v-u)/t
(i) A body is moving with initial velocity u then,
m(v-u)/t = 0 ⇒ v – u = 0
∴ v = u
Thus, final velocity is also same.
(ii) A body is at rest i.e., u = 0
Therefore, from above u = v = 0
So, the body will continue to be at rest.