Question

When nomentum is increased by 3 times its k.E becomes?

Answer 1

KE = mv*v/2 = p*v/2. KE is directly proportional with p, KE ∝ p. The correlation coefficient is v/2.

P = mv. When p double, the m cannot change but only v can change: 2p = 2v*m.

The KE of this tripled p is: (3v*m)* 3v/2 = m (3v)²/2 = m*9v²/2 = 9mv²/2 , which is 9 KE.

So when p * 3, its KE * 9.

The rule is: how many times the p changed, its corresponding times of the KE changed are the square of the times the p changed.

The reason is: any v change in p, there will be a corresponding change of v² in KE.