Heavy projectile, light target: A heavy particle (mass M) with velocity V has a
ID: 1495285 • Letter: H
Question
Heavy projectile, light target: A heavy particle (mass M) with velocity V has a perfectly elastic head-on collision with a resting very light particle of mass m. Assuming M >> m (i.e. m ~ 0), find the final velocities of the projectile (M) and the target particle (m) in terms of V. Suppose a heavy particle (mass M) with velocity V has a perfectly elastic head-on collision with a very light particle of mass m moving with the same speed in opposite direction so its velocity is -V. Assuming M >> m (i.e. m ~ 0), find the final velocities of the projectile (M) and the target particle (m) in terms of V.Explanation / Answer
2)
mass of he heavy particle is m1= M, velocity is u1=V
mass of the ligter particle is m2=m (at rest) u2=0
after collision,
velocity of the particle M is v1
velocity of the particle m is v2
use,
v1=u1*(m1-m2)/(m1+m2) + 2*m2*u2/(m1+m2)
and
v2=u2*(m1-m2)/(m1+m2) + 2*m1*u1/(m1+m2)
now,
v1=u1*(m1-m2)/(m1+m2)
and
M>>m
V1=V*M/(M)
==>
after collision velocity of the M is V1=V --------->
and
v2=2M*u1/M
V2=2*u1
V2=2*V
after collision velocity of the m is V2=2V --------->
3)
use,
v1=u1*(m1-m2)/(m1+m2) + 2*m2*u2/(m1+m2)
v1=V*(M-m)/(M+m) - 2*m*V/(M+m)
V1=V*(M/M) - 2*m*V/M
V1=V
===> after collision velocity of the M is V1=V
and
v2=u2*(m1-m2)/(m1+m2) + 2*m1*u1/(m1+m2)
v2=-V*M/(M)
V2=-V
===> after collision velocity of the M is V2=-V
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.