Physics

Problem

(Long-answer question) Two bodies of masses

m_1

and

m_2

move along the same straight line with speeds

u_1

and

u_2

(

u_1>u_2

) and collide such that they stick together after impact. (i) Derive an expression for the loss of kinetic energy

\Delta K

in terms of

m_1,\;m_2,\;u_1

and

u_2

. (ii) Hence obtain the fractional loss of kinetic energy when the bodies have masses

m

and

3m

, the lighter body (

m

) being the one in motion with speed

u

while the heavier body (

3m

) is initially at rest. (iii) Explain why the collision described is categorised as perfectly inelastic and comment on the magnitude of energy loss obtained in part (ii). a. (i) Derive an expression for the loss of kinetic energy

\Delta K

in terms of

m_1,\;m_2,\;u_1

and

u_2

when the bodies stick together after collision. b. (ii) Hence obtain the fractional loss of kinetic energy when the bodies have masses

m

and

3m

, the lighter body (

m

) moving with speed

u

and the heavier body initially at rest.

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