Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

Elastic Collision
REVIEW OF PHYSICAL PRINCIPLES 27
An elastic collision is defined as a collision between two bodies in which kinetic
energy and momentum are conserved; that is, the sum of the kinetic energy of the
two bodies before the collision is equal to their sum after the collision, and the sums
of their momenta before and after the collision are the same. In an elastic collision,
the total kinetic energy is redistributed between the colliding bodies; one body gains
energy at the expense of the other. A simple case is illustrated in the example below.
W EXAMPLE 2.12
A block of mass 10 kg, made of a perfectly elastic material, slides on a frictionless
surface with a velocity of 2 m/s and strikes a stationary elastic block whose mass is
2 kg (Fig. 2-8). How much energy was transferred from the large block (M) tothe
small block (m) during the collision?
Solution
If V1,v1, andV2 and v2 are the respective velocities of the large and small blocks
before and after the collision, then, according to the laws of conservation of energy
and momentum, we have
and
1 2 1
MV1 +
2 2 mv2
1
1 =
2 MV 2 1
2 +
2 mv2 2
MV1 + mv1 = MV2 + mv2
Since v1 = 0, Eqs. (2.41) and (2.42) may be solved simultaneously to give
V2 = 1 1 m
3 s and v2 = 3 1 m
3 s .
The kinetic energy transferred during the collision is
1 2 1
MV1 −
2 2 MV 2 2
1
= × 10 4 −
2 16
= 11
9
1
9 J,
(2.41)
(2.42)
Figure 2-8. Elastic collision between blocks M and m, in which the sum of both kinetic energy and
momenta of the two blocks before and after the collision are the same.