A particle of mass $$m1$$ collides $$head-on$$ with another stationary particle of mass $$m2$$ $$m2$$$$m1$$. The collision is perfectly inelastic. The fraction of kinetic energy which is converted into heat in this collision is

Question

A particle of mass $$m1$$ collides $$head-on$$ with another stationary particle of mass $$m2$$ $$m2$$>$$m1$$. The collision is perfectly inelastic. The fraction of kinetic energy which is converted into heat in this collision is

Infinity Learn · Accepted Answer

For conservation of momentum, we have,$$m1v1=m1+m2v$$ or $$v=m1/m1+m2v1$$​ Now the loss of energy $$=Ki$$−$$Kf=12m1v12$$−$$12m1+m2v2$$​∴ Fraction of energy $$lost=Ki$$−KfKi ​$$=12m1v12$$−$$12m1+m2v212m1v1$$                                                             $$=1$$−$$m1+m2/m1$$×$$v2/v12$$​$$=1$$−$$m1+m2/m1$$×$$m1v12/m1+m22$$×$$1/v12$$​$$=1$$−$$m1m1+m2=m2/m1+m2$$

A particle of mass $m_{1}$ collides head-on with another stationary particle of mass $m_{2} (m_{2} > m_{1})$ . The collision is perfectly inelastic. The fraction of kinetic energy which is converted into heat in this collision is

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A particle of mass m1 collides head-on with another stationary particle of mass m2 m2>m1. The collision is perfectly inelastic. The fraction of kinetic energy which is converted into heat in this collision is

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A particle of mass $m_{1}$ collides head-on with another stationary particle of mass $m_{2} (m_{2} > m_{1})$ . The collision is perfectly inelastic. The fraction of kinetic energy which is converted into heat in this collision is