Question

CalculAte the kinetic energy if the momentum increase 30%

Answer 1

According to the given problem,

The momentum of a body increase by 30%. What is the percentage increase in kinetic energy?

Let M denotes the mass of the given body.

Let (K1, P1) & (K2, P2) denote respectively initial & final values of (kinetic energy, linear momentum).

So we have the following relations,

P2 = (1 + 30/100)*P1 = 1.3*P1 …… (1a)

K1 = (P1)^2/(2*M) …… (2a) [we know, p = mv, hence KE = mv^2/2 = p^2/(2m)]

K2 = (P2)^2/(2*M) …… (2b)

Hence from (2a) & (2b) we get,

K2 / K1 = (P2)^2 / (P1)^2 = 1.3^2 [from (1a)]

or K2 = 1.69*K1 = (1 + 69/100)*K1 …… (2c)

Therefore it is evident from (2c) that

the percentage increase in kinetic energy = 69% [Ans]

Answer 2

According to the given problem,

The momentum of a body increase by 30%. What is the percentage increase in kinetic energy?

Let M denotes the mass of the given body.

Let (K1, P1) & (K2, P2) denote respectively initial & final values of (kinetic energy, linear momentum).

So we have the following relations,

P2 = (1 + 30/100)*P1 = 1.3*P1 …… (1a)

K1 = (P1)^2/(2*M) …… (2a) [we know, p = mv, hence KE = mv^2/2 = p^2/(2m)]

K2 = (P2)^2/(2*M) …… (2b)

Hence from (2a) & (2b) we get,

K2 / K1 = (P2)^2 / (P1)^2 = 1.3^2 [from (1a)]

or K2 = 1.69*K1 = (1 + 69/100)*K1 …… (2c)

Therefore it is evident from (2c) that

the percentage increase in kinetic energy = 69% [Ans]