Momentum and
Collisions
Newton’s 1st Law of Motion
 “An
object at rest will stay at rest,
and an object in motion will stay in
motion unless acted upon by a net
force.”
 Also
known as the Law of Inertia.
Inertia
 Inertia
is the tendency of an object
to resist changes in motion.
 An
object’s mass determines its
inertia.
Momentum
 The
linear momentum of an object of
mass m moving with velocity v is
defined as the product of the mass
and the velocity. Momentum is
represented by the symbol p.
p=mv
p = momentum of object (kg m/s)
m = mass of object ( kg)
v = velocity of object (m/s)
Momentum
 The
SI unit of momentum is kg m/s.
Sample Problem
 Determine
the
momentum of a
60-kg halfback
moving eastward
at 9 m/s.
Sample Problem
Givens:
m = 60 kg
v = 9 m/s
Formula:
p=mv
Solution:
p = (60 kg)(9 m/s) = 540 kg m/s
The momentum of the halfback is 540 kg m/s.
Solve These Problems:
1. What is the momentum of a 1000 kg car
travelling at 25 m/s? 25,000 kg m/s
2. What is the momentum of a 250 kg
skater moving at 6 m/s? 1500 kg m/s
3. What is the velocity of a 5000 kg truck
that has momentum of 100,000 kg m/s?
20 m/s
Newton’s 2nd Law of Motion
 The
F
Law of Acceleration
= ma
Impulse
 Newton’s
2nd Law of Motion as it
relates to momentum becomes:
FΔt = Δp
FΔt is the impulse and Δp is
the change in linear momentum.
 where
Impulse
Ft  p
 In
simple terms, a small force acting
for a long time can produce the same
change in momentum as a large
force acting for a short time.
Effect of Collision Time Upon
the Force
Racket and Bat Sports
 The
act of following through
when hitting a ball increases
the time of collision and
contributes to an increase in
the velocity change of the
ball.
 In tennis, baseball, racket
ball, etc., giving the ball a
high velocity often leads to
greater success.
Newton’s 3rd Law of Motion
 “For
every action there is an equal
and opposite reaction.”
 Consider a pair of objects
interacting with each other.
 According to Newton’s 3rd Law, the
forces they exert on each other
must be equal and opposite.
Conservation of Momentum
 In
every interaction between two
isolated objects, the change in
momentum of the first object is equal
to and opposite to the change in
momentum of the second object.
 Thus in all interactions between two
isolated objects, momentum is
conserved.
Law of Conservation of
Momentum

To solve conservation of momentum
problems, use the formula:
pbefore  pafter

The sum of the momenta before the
collision equals the sum of the momenta
after the collision.
Total Momentum
 The
momentum of each object
could change before and after an
interaction, but the total
momentum of the two objects
together remains constant.
Three Types of Problems

Explosion
 Both
objects at rest before the collision
 Objects move off in opposite directions

Two objects in motion – Elastic Collision
 Objects
have initial velocity (one may be at rest)
 After collision objects have different velocities

Objects move together - Inelastic Collision
 One
or more objects in motion before collision
 After collision, objects move together with same
velocity (This could be reversed.)
p  p'
m1v1  m2v2  m v  m v
'
1 1
'
2 2
p = momentum before collision (kg m/s)
p’ = momentum after collision (kg m/s)
m1 = mass of object 1 (kg)
v1 = velocity of object 1 before the collision (m/s)
m2 = mass of object 2 (kg)
v2 = velocity of object 2 before the collision (m/s)
v1’ = velocity of object 1 after the collision (m/s)
v2’ = velocity of object 2 after the collision (m/s)
Head-On Collision
Car “Rear Ends” Truck
Truck “Rear-Ends” Car
The Cart and the Brick
Sample Problem
Two skaters stand facing each other. One
skater’s mass is 60 kg, and the other’s
mass is 72 kg. If the skaters push away
from each other without spinning,
 a. the 60 kg skater travels at a lower
momentum.
 b. their momenta are equal but opposite.
 c. their total momentum doubles.
 d. their total momentum decreases.
