Physics

Problem

Answer the following questions concerning the relationship between linear momentum

p

and kinetic energy

K

. a. (i) Starting from the definitions of

p

and

K

, derive an expression for

p

in terms of

K

and the mass

m

of a particle. b. (ii) Two particles

P

and

Q

have equal kinetic energies but their masses are in the ratio

m_P:m_Q = 1:4

. Using the expression obtained in part (i), find the ratio of their momenta

p_P:p_Q

. c. (iii) Conversely, two other particles

R

and

S

have equal momenta, while their masses are again in the ratio

1:4

. Find the ratio of their kinetic energies

K_R:K_S

. d. (iv) Comment on the results obtained in parts (ii) and (iii) to explain how two bodies can have equal kinetic energies but unequal momenta, and vice-versa.

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