A body of mass m 1 with initial velocity v 0 collides with a second body, of mas

Question

A body of mass m1 with initial velocity v0 collides with a second body, of mass m2, initially at rest (like in the LAB frame). The initial Kinetic energy K0 of the first body must be "paid for"(must be provided by some energy source). But it is the total kinetic energy of the two bodies in the center-of-mass(CM) frame which represents the energy available for reactions, to create new particles, et cetera. Calculate the ratio of this total energy to the initial LAB energy K0, in term of the masses m1 and m2.

Explanation / Answer

K0=0.5*m1*v0^2
after collison, conserving momentum:
speed=m1*v0/(m1+m2)
final kinetic energy=0.5*(m1+m2)*(m1*v0/(m1+m2))^2=0.5*m1^2*v0^2/(m1+m2)

so ratio=1/(m1+m2)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.