PHYS 1114: Physics I
Lecture 7:
Linear Momentum &
Collisions
Professor Kenny L. Tapp
Linear Momentum
The linear momentum of an object is the product
of its mass and velocity.
p=mv
Note that momentum is a vector—it has both a magnitude and a direction.
Quick Question 1:
Which has more linear momentum?
(a) a 1500 kg car moving at 25.0 m/s
or
(b) a 40,000 kg truck moving at 1.00 m/s
SI unit of momentum: kg • m/s. This unit has no special name.
Linear Momentum
For a system of objects, the total momentum is the vector sum of each.
Linear Momentum
The change in momentum is the difference between the momentum vectors.
Conservation of Linear Momentum
If there is no net force acting on a system, its total
momentum cannot change.
This is the law of conservation of momentum.
If there are internal forces, the momenta of individual
parts of the system can change, but the overall
momentum stays the same.
Quick Question 3:
Conservation of Linear Momentum
Collisions happen quickly
enough that any external
forces can be ignored
during the collision.
Therefore, momentum is
conserved during a
collision.
Quick Question 3:
Starting from rest, two skaters
push off against each other on
ice where friction is negligible.
One is a 54-kg woman and
one is a 88-kg man. The
woman moves away with a
speed of +2.5 m/s. Find the
recoil velocity of the man.
Quick Question 4:
A 60 kg astronaut floating at rest in space outside a
space capsule throws his 0.50 kg hammer such that it
moves with a speed of 10 m/s relative to the capsule.
Knowing the astronaut will move in the opposite
direction of the hammer, due to the conservation of
momentum, what is the astronaut’s velocity?
Elastic and Inelastic Collisions
In an elastic collision,
the total kinetic
energy is conserved.
Total kinetic energy is
not conserved in an
inelastic collision.
Elastic and Inelastic Collisions
Elastic and Inelastic Collisions
• Consider a collision in 2-D (cars crashing at a slippery
intersection...no friction).
V$
v1
A completely inelastic
collision is one where
the objects stick
together afterwards.
m1$+$m2
m1
m2
v2$
before
Elastic and Inelastic Collisions
a'er
Elastic and Inelastic Collisions
For an elastic collision, both the kinetic energy and the
momentum are conserved:
Example Diagram
Elastic and Inelastic Collisions
Collisions may take
place with the two
objects approaching
each other, or with
one overtaking the
other.
Quick Question 5:
Bobby Boucher (m = 115 kg) tackles his Professor
in class with a running velocity of +4.5 m/s. The
two move off together with a velocity of +2.6 m/s.
Find the mass of the Professor.
Quick Question 6:
An Audi (m = 1500kg) moving at 24 m/s collides
inelastically with a Porsche(m = 2000kg) traveling at
18 m/s in the same direction. Find the velocity of the
two-vehicle combination immediately after the collision.
Quick Question 7:
James Bond (mass 91 kg) jumps
down from a digger onto a train
(mass 510 kg) in which a criminal is
fleeing. The velocity of the train is
initially 35 m/s. What is the velocity
of the train after James Bond lands
in it?
Jet Propulsion and Rockets
If you blow up a balloon and then let it go, it zigzags away from you
as the air shoots out. This is an example of jet propulsion. The
escaping air exerts a force on the balloon that pushes the balloon in
the opposite direction.
Jet propulsion is another example of
conservation of momentum.
Conservation of Momentum
The thrust of a rocket works the same way.
Conservation of Momentum
Conservation of Momentum
This same phenomenon explains the recoil of a gun:
Quick Question 8:
A rifle with a mass of 3.06 kg fires a 0.05 kg
bullet with a speed of 300 m/s.
(a) Find the recoil speed of
the rifle.
(b) If a 71.43 kg hunter holds
the rifle firmly against his
shoulder, find the recoil speed
of the man and rifle.