TYPES OF COLLISION
❑ Elastic Collision
▪ both momentum and
kinetic energy are
conserved.
▪ Example: billiard ball
TYPES OF COLLISION
❑ Elastic Collision
𝒎𝟏 𝒗𝟏 + 𝒎𝟐 𝒗𝟐 = 𝒎𝟏 𝒗𝟏 ′ + 𝒎𝟐 𝒗𝟐 ′
𝟏 𝟏 𝟏 𝟏
𝒎𝟏 𝒗𝟏 ² + 𝒎𝟐 𝒗 𝟐 ² = 𝒎𝟏 𝒗𝟏 ′² + 𝒎𝟐 𝒗𝟐 ′²
𝟐 𝟐 𝟐 𝟐
TYPES OF COLLISION
❑ Inelastic Collision
❑ May stick together and move as a single mass
due to deformation.
❑ The kinetic energy is not conserved, as some is
transformed into deformation, heat, and sound.
𝒎𝟏 𝒗𝟏 + 𝒎𝟐 𝒗𝟐 = 𝒎𝟏 𝒗𝟏 ′ + 𝒎𝟐 𝒗𝟐 ′
TYPES OF COLLISION
❑ Perfectly Inelastic
Collision
▪ Occur when the two
objects stick together
after the collision so that
the objects have the
same final velocity.
TYPES OF COLLISION
❑ Perfectly Inelastic Collision
𝒎𝟏 𝒗𝟏 + 𝒎𝟐 𝒗𝟐 = (𝒎𝟏 + 𝒎𝟐 )𝒗′
EXAMPLE 1
A 2-kg bowling ball moves to the right at
20 m/s and collides a stationary 3.5 kg
bowling ball. What will be final velocity of
the balls after the collision?
Check your Understanding
1
3
COEFFICIENT OF RESTITUTION (e)
• IS THE NEGATIVE RATIO OF THE VELOCITY OF TWO COLLIDING BODIES
AFTER COLLISION TO THE RELATIVE VELOCITY BEFORE COLLISION.
𝑣𝐴2 𝑣𝐵2
e= − −
(𝑣𝐴1 𝑣𝐵1
− )
•Elastic collision- has a coefficient of restitution of 1
•Inelastic collision – has a coefficient of restitution between 0
and 1
•Perfectly inelastic collision-has a coefficient of restitution of 0
EXAMPLE
1. Two balls A and B are approaching each other with velocities 4.5 n/s and
7.2 m/s, respectively. The mass of ball A is 3.2 kg, while that of ball B is 5.6
kg. (a) find the velocity of the two bodies after impact, assuming that the
collision is perfectly inelastic. (b) Find the kinetic energy lost during
collision.
2. Supposed the collision in item 1 is elastic. Find (a) how much kinetic
energy is lost and (b) how fast each ball is moving after colliding.
EXAMPLE 3
Car A of mass 2500kg moving at a velocity of
12.0m/s toward east collides with car B of mass
3000kg moving at a velocity of 15.0m/s toward
north. After the crash, the two cars stick
together. Both of the cars were deformed. 12.0 m/s
a. What is the velocity of the cars immediately
after the impact?
b. How much of the energy was absorbed by
the deformation of the two cars? 15.0 m/s
EXAMPLE 4
A 7500 kg truck travelling at 5.0 m/s east collides with a
1500 kg car moving at 25 m/s in a direction 20° south of
west. After collision, the two vehicles remain tangled
together. With what speed and in what direction does the
wreckage begin to move?
CHECK YOUR UNDERSTANDING
1. A 5-kg lump of clay moving at 10 m/s to the left
strikes a 6-kg lump of clay at 12 m/s to the right. The
two lamps stick together.
(a) Find the final speed after collision.
(b)Find the kinetic energy dissipated.
2. A car with mass 1.8 x 10³ kg is traveling east at
25.0 m/s collides at an intersection with a 2.5 x 10³
kg van traveling north at 20.0 m/s. Find the
magnitude and direction of the velocity of the
entangled vehicles after the collision, assuming that
the friction between the vehicles and road can be
neglected.
