Two objects moving with a speed v travel in oppositedirections in a straight lin

Question

Two objects moving with a speed v travel in oppositedirections in a straight line. The objects stick together when theycollide, and move with a speed of v/10 after the collision. (a) What is the ratio of the final kineticenergy of the system to the initial kinetic energy?
1
(b) What is the ratio of the mass of the more massive object to themass of the less massive object?
2 (a) What is the ratio of the final kineticenergy of the system to the initial kinetic energy?
1
(b) What is the ratio of the mass of the more massive object to themass of the less massive object?
2

Explanation / Answer

Initially: E = (1/2)mv2 + (1/2)Mv2 E = (1/2)v2(m+M) After: E' = (1/2)(m+M)(v/10)2 E' = (1/200)v2(m+M) E'/E = (1/200)v2(m+M) /(1/2)v2(m+M) = 2/200 =1/100 b) Use cons. of momentum, letting m be the larger mass andtherefore initially moving in the positive direction: mv + M(-v) = (m+M)(v/10) mv - Mv = mv/10 + Mv/10 mv - mv/10 = Mv/10 + Mv m(v-v/10) = M(v/10 + v) m/M = (v+v/10)/(v-v/10) m/M = (1+1/10)/(1-1/10) m/M =11/9 E' = (1/200)v2(m+M) E'/E = (1/200)v2(m+M) /(1/2)v2(m+M) = 2/200 =1/100 b) Use cons. of momentum, letting m be the larger mass andtherefore initially moving in the positive direction: mv + M(-v) = (m+M)(v/10) mv - Mv = mv/10 + Mv/10 mv - mv/10 = Mv/10 + Mv m(v-v/10) = M(v/10 + v) m/M = (v+v/10)/(v-v/10) m/M = (1+1/10)/(1-1/10) m/M =11/9

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