Elastic collisions
r r
pi = p f
r
r
r
r
Kinetic Energy is conserved. m1v1i + m2v2 i = m1v1 f + m2 v2 f
Momentum is conserved .
KEi = KE f
m1v 21i + m2 v2 2 i = m1v 21 f + m2v 2 2 f
So in an elastic collision, particles bounce off each other
without loss of kinetic energy.
Usually such collisions are approximate!
Quiz
Inelastic collisions
Momentum is conserved .
Kinetic Energy is NOT conserved.
r
r
pi = p f
r
r
r
r
m 1v 1 i + m 2 v 2 i = m 1 v 1 f + m 2 v 2 f
So in an inelastic collision, particles bounce off each other
with a loss of kinetic energy!
The lost kinetic energy is converted into thermal or internal
energy.
A completely inelastic collision is one where the particles
stick together. (also called a perfectly inelastic collision)
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Elastic versus Inelastic collisions
Momentum is conserved (unless there is an external
force)
Kinetic Energy is conserved only in an elastic collision
Inelastic: r
r
pi = p f
r
r
r
r
m 1v 1i + m 2 v 2 i = m 1 v 1 f + m 2 v 2 f
Elastic:
m1v 21i + m2 v2 2 i = m1v 21 f + m2v 2 2 f
m 1v 1iy + m 2 v 2 iy = m 1 v1 fy + m 2 v 2 fy
m 1 v1 iz + m 2 v 2 iz = m 1 v1 fz + m 2 v 2 fz
m 1 v1ix + m 2 v 2 ix = m 1 v1 fx + m 2 v 2 fx
Perfectly inelastic collision of two particles
r r
pi = p f
r
r
r
m1v1i + m2v2 i = (m1 + m2 )v f
Notice that p and v are
vectors and, thus have a
direction (+/-)
K i = K f + Eloss
There is a loss
1
1
1
2
2
2
m1v1i + m 2 v2 i = ( m1 + m 2 )v f + Eloss in energy Eloss
2
2
2
Perfectly inelastic collision of two particles II
r
r
r
m1v1i + m2 v2i = ( m1 + m2 )v f
r
r
r
m1v1i + m2 v2 i
vf =
( m1 + m2 )
What if one particle was
initially stationary?
r
vf =
r
m2 v2 i
( m1 + m2 )
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Example I
Ballistic Pendulum:
In a ballistic pendulum a bullet (0.1 kg) is fired into a block (0.5 kg) that is
suspended from a light string. The block (with the bullet stuck in it) is lifted
up by 0.051 m.
(a) What is the speed of the combined bullet/pendulum right after the collision?
(b) Find the initial speed of the bullet?
(c) Find the loss in mechanical energy due to the collision
Example 2
Accident investigation. Two
automobiles of equal mass approach
an intersection. One vehicle is
traveling towards the east with 29 mi/h
13.0 m/s
(13.0 m/s) and the other is traveling
north with unknown speed. The
vehicles collide in the intersection and
stick together, leaving skid marks at an
angle of 55º north of east. The second
driver claims he was driving below the
speed limit of 35 mi/h (15.6 m/s).
??? m/s
Is he telling the truth?
What is the speed of the “ combined vehicles” right after the collision?
How long are the skid marks (µk = 0.5)
Quiz
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Quiz
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