CHAPTER 3 MOMENTUM AND IMPULSE

Chapter --- Momentum & Impulse

Momentum
& Impulse

Momentum Conservation
& Impulse of Linear

Momentum

Momentum Impulse Collision

Elastic Inelastic

Chapter --- Momentum & Impulse

3.1 MOMENTUM & IMPULSE

(a) Define momentum & impulse

J  Ft

(a) Solved problem related to impulse-momentum
theorem,

J  p  mv f  mvi

(a) Use F-t graph to determine impulse

Chapter --- Momentum & Impulse

Linear Momentum

1. Momentum is the product between mass and velocity,
Ԧ = Ԧ

2. Momentum is vector quantity; Unit: kg m s-2

3. It’s direction of the momentum is the same as the direction of the velocity

4. Extra information : Can be resolved into vertical (y) & horizontal (x)
components

py  px  p cosθ  mv cosθ
p
py  p sin θ  mvsin θ

px

3.1: MOMENTUM & IMPULSE

Chapter --- Momentum & Impulse

The greater an object’s momentum, the more force needed to
stop it

Both are hard to stop. Charging elephant has great mass, single
bullet has high velocity

3.1: MOMENTUM & IMPULSE

Chapter --- Momentum & Impulse

Impulse, Ԧ F  ma
F  mv  mu
From the equation F=ma ,
t
Ft  mv  mu

 change in momentum

Hence, Impulse, J = the product of force,F and time,t

= change in momentum

J  Ft  p  p f  pi

J  Ft  p  mv  mu

Unit: Impulse • vector quantity
N s or kg m s1
• direction is the same as the
constant force on the object

3.1: MOMENTUM & IMPULSE

Chapter --- Momentum & Impulse

When two objects in collision, the impulsive force, F against
time, t graph is given by the Figure 3.2.

F

Figure 3.2 0 t1 t2 t

Shaded area under the Ft graph = impulse

3.1: MOMENTUM & IMPULSE

Chapter --- Momentum & Impulse

p  mv

J  Ft  p  mv  mu
 m( v  u )

J  area under

F - t graph

Chapter --- Momentum & Impulse

3.2 CONSERVATION of
LINEAR MOMENTUM

(a) State the principle of conservation of linear
momentum

(b) Apply the principle of conservation of linear
momentum in the elastic and inelastic collisions in
1D and 2D collisions.

(c) Differentiate elastic and inelastic collisions

Chapter --- Momentum & Impulse

Principle of
Conservation of

Momentum

states “In an isolated
(closed) system, the
total momentum of that
system is constant.”

“When the net external
force on a system is zero,
the total momentum of
that system is constant.”

3.2: CONSERVATION OF LINEAR MOMENTUM

Chapter --- Momentum & Impulse

Collision

 is defined as an isolated event in which two or more
bodies (the colliding bodies) exert relatively strong
forces on each other for a relatively short time.

Collision

Elastic Inelastic

3.2: CONSERVATION OF LINEAR MOMENTUM

Chapter --- Momentum & Impulse

Elastic collision

• is defined as one in which the total kinetic energy (as well as
total momentum) of the system is the same before and after
the collision

Before collision m1u1 m2u2

12

At collision 12

After collision m1v1 1 m2v2

3.2: CONSERVATION OF LINEAR MOMENTUM 2

Chapter --- Momentum & Impulse

Properties of elastic collision

The total energy is  Ei   E f
conserved
    
The total momentum is pi pf
conserved
 Ki   K f
The total kinetic energy is
conserved

1 m1u12  1 m2u22  1 m1v12  1 m2v22
2 2 2 2

Chapter --- Momentum & Impulse

Inelastic (non-elastic) collision

• is defined as one in which the total kinetic energy of the system
is not the same before and after the collision (even though the
total momentum of the system is conserved)

m1u1 u2  0 m2

Before collision

12

Caution

At collision 12 • Not all the inelastic collision is
12 stick together.
After collision
(stick together) • In fact, inelastic collisions
include many situations in
which the bodies do not stick.

v

3.2: CONSERVATION OF LINEAR MOMENTUM

Chapter --- Momentum & Impulse

Properties of inelastic collision

The total energy is  Ei   E f
conserved
    
The total momentum is pi pf
conserved

The total kinetic energy is Ki  Kf
conserved

The total kinetic • some of the energy is converted to internal energy
energy is not and some of it is transferred away by means of
conserved sound or heat
because

3.2: CONSERVATION OF LINEAR MOMENTUM

Chapter --- Momentum & Impulse

Case study 1:

Type of collision and why?

3.2: CONSERVATION OF LINEAR MOMENTUM

Chapter --- Momentum & Impulse

Case study 2:

Type of collision and why?

3.2: CONSERVATION OF LINEAR MOMENTUM

Chapter --- Momentum & Impulse

THE END…

Next Chapter…

CHAPTER 4:
FORCES