It's obvious that a body of mass 100m, colliding with a body of mass m,
can only slow down but not stop in place and bounce back!
No, it's not obvious, in fact it's not even always true. Here's a
specific example where the body of mass 100m *does* bounce back:
Suppose we have
body A: mass m_A=100 kg, initial velocity v_A1=+1 m/s (moving right)
body B: mass m_B=1 kg, initial velocity v_B1=-1000 m/s (moving left)
and these bodies have an elastic collision at position x=0 m and t=0 s.
The formulas in the previously-cited Wikipedia article
<https://en.wikipedia.org/wiki/Elastic_collision> give the final
velocities after the collision as:
v_A2 = -18.822 m/s (body A recoils to the left)
v_B2 = +982.178 m/s (body B recoils to the right)
But we don't have to trust the Wikipedia article! We can check for
ourselves whether or not these v_A2 and v_B2 are correct by checking
whether or not both linear momentum and kinetic energy are conserved:
Linear momentum:
before the collision: m_A*v_A1 + m_B*v_B1 = -900 kg m/s
after the collision: m_A*v_A2 + m_B*v_B2 = -900 kg m/s
i.e., linear momentum is conserved.
Kinetic energy:
before the collision: 1/2 m_A*v_A1^2 + 1/2 m_B*v_B1^2 = 500050 Joules
after the collision: 1/2 m_A*v_A2^2 + 1/2 m_B*v_B2^2 = 500050 Joules
i.e., kinetic energy is conserved.
Since we find that these values of v_A2 and v_B2 conserve both linear
momentum and kinetic energy, we know that these are in fact the correct
v_A2 and v_B2 for an elastic collision.
From the initial & final velocities, it's easy to calculate the
bodies' positions:
t (s) x_A (m) x_B(m)
-3 -3.0 +3000.0
-2 -2.0 +2000.0
-1 -1.0 +1000.0
0 0.0 0.0 (collision happens here)
+1 -18.822 +982.178
+2 -37.644 +1964.356
+3 -56.465 +2946.535
So in this case, yes, a body of mass 100 kg does "bounce back" (final
velociity is of the opposite sign to initial velocity) after colliding
with a body of mass 1 kg.
--
-- "Jonathan Thornburg [remove -color to reply]" <dr.j.thornburg@gmail-pink.com>
(he/him; on the west coast of Canada)
"All models are wrong, but some are useful" -- George E. P. Box
| Date | Sujet | # | Auteur | |
| 11 Feb 26 |  Elastic Collision | 15 | Luigi Fortunati | |
| 13 Feb 26 |  Re: Elastic Collision | 5 | Luigi Fortunati | |
| 13 Feb 26 |   Re: Elastic Collision | 1 | Mikko | |
| 13 Feb 26 | Re: Elastic Collision | 1 | Petri Kaukasoina | |
| 13 Feb 26 | Re: Elastic Collision | 1 | Pierre Asselin | |
| 15 Feb 26 |  Re: Elastic Collision | 1 | Luigi Fortunati | |
| 15 Feb 26 | Re: Elastic Collision | 1 | Jonathan Thornburg [remove -color to reply] | |
| 15 Feb 26 | Re: Elastic Collision | 1 | Jonathan Thornburg [remove -color to reply] | |
| 16 Feb 26 | Re: Elastic Collision | 7 | Luigi Fortunati | |
| 28 Feb 26 |  Re: Elastic Collision | 1 | Luigi Fortunati | |
| 28 Feb 26 | Re: Elastic Collision | 1 | Mikko | |
| 5 Mar 26 | Re: Elastic Collision | 1 | Luigi Fortunati | |
| 8 Mar 26 | Re: Elastic Collision | 1 | Mikko | |
| 12 Mar 26 | Re: Elastic Collision | 1 | Luigi Fortunati | |
| 16 Mar 26 | Re: Elastic Collision | 1 | Mikko |
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