Chapter 2.
4 Momentum
Chapter 2.4 Momentum
Momentum
1.
Momentum is defined as the product of mass and velocity.
2.
Momentum is a vector quantity. It has both magnitude and
direction.
The SI unit of momentum is kgms-1
3.
4. Principle of Conservation of Momentum
The principle of conservation of momentum states that in a system make out of
objects that react (collide or explode), the total momentum is constant if no external
force is acted upon the system.
Sum of Momentum Before Reaction = Sum of Momentum After Reaction
5. Elastic Collision
Elastic collision is the
collision where
the kinetic energy is
conserved after the
collision.
Total Kinetic Energy
before Collision
= Total Kinetic Energy
after Collision
Additional notes:
In an elastic collision, the 2 objects separated right after the collision, and
the momentum is conserved after the collision.
Total energy is conserved after the collision.
Chapter 2.4 Momentum
6. Inelastic Collision
Inelastic collision is the
collision where
the kinetic energy is not
conserved after the
collision.
Additional notes:
In a perfectly elastic
collision, the 2 objects
attach together after the
collision, and
the momentum is also conserved after the collision.
Total energy is conserved after the collision.
Formula
Example 1 - Both Object are in the Same Direction
before Collision
A Car A of mass 600 kg moving at 40 ms-1 collides with a car B
of mass 800 kg moving at 20 ms-1 in the same direction. If car
B moves forwards at 30 ms-1 by the impact, what is the
velocity, v, of the car A immediately after the crash?
Answer:
m1 = 600kg
m2 = 800kg
u1 = 40 ms-1
u2 = 20 ms-1
v1 = ?
v2 = 30 ms-1
Chapter 2.4 Momentum
Example2 - Both Object are in opposite direction Before
Collision
A 0.50kg ball traveling at 6.0 ms-1 collides head-on with a 1.0
kg ball moving in the opposite direction at a speed of 12.0 ms -1.
The 0.50kg ball moves backward at 14.0 ms-1 after the
collision. Find the velocity of the second ball after collision.
Answer:
m1 = 0.5 kg
m2 = 1.0 kg
u1 = 6.0 ms-1
u2 = -12.0 ms-1
v1 = -14.0 ms-1
v2 = ?
Example 3 - Perfectly Inelastic Collision:
A lorry of mass 8000kg is moving with a velocity of 30 ms -1.
The lorry is then accidentally collides with a car of mass
1500kg moving in the same direction with a velocity of 20 ms -1.
After the collision, both the vehicles attach together and move
with a speed of velocity v. Find the value of v.
Answer:
(IMPORTANT: When 2 object attach together, they move with
same speed.)
m1 = 8000kg
m2 = 1500kg
u1 = 30 ms-1
u2 = 20 ms-1
v1 = v
v2 = v
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Explosion
Before explosion both object stick
together and at rest.
After collision, both object move at
opposite direction.
Total Momentum before collision Is
zero
Total Momentum after collision :
m1v1 + m2v2
Chapter 2.4 Momentum
From the law of conservation of momentum:
Total Momentum Before collision = Total Momentum after collision
0 = m1v1 + m2v2
m1v1 = - m2v2
(-ve sign means opposite direction)
Example:
A man fires a rifle which has mass of 2.5 kg. If the mass of the
bullet is 10 g and it reaches a velocity of 250 m/s after
shooting, what is the recoil velocity of the pistol?
Answer:
This is a typical question of explosion.
m1 = 2.5 kg
m2 = 0.01 kg
u1 = 0 ms-1
u2 = 0 ms-1
v1 = ?
v2 = 250 ms-1
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Chapter 2.4 Momentum
Application use the Momentum
Rocket
1.
Mixture of hydrogen and oxygen fuels burn in the combustion chamber.
2.
Hot gases are expelled through the exhausts at very high speed .
3.
The high-speed hot gas produce a high momentum backwards.
4.
By conservation of momentum, an equal and opposite momentum is
produced and acted on the rocket, pushing the rocket upwards.
Jet Engine
1.
Air is taken in from the front and is compressed by the compressor.
2.
Fuel is injected and burnt with the compressed air in the combustion
chamber.
3.
The hot gas is forced through the engine to turn the turbine blade,
which turns the compressor.
4.
5.
High-speed hot gases are ejected from the back with high momentum.
This produces an equal and opposite momentum to push the jet plane
forward.
Chapter 2.4 Momentum
