Chapter 6
Momentum and Collisions
1.
Momentum and Impulse
2.
Conservation of Momentum
3.
1D Collisions
4.
2D Collisions
1
Momentum
What is momentum?
How do I represent it?
How do I calculate it?
What are the SI units?
2
Impulse
What is impulse?
How do I calculate it?
What are its SI units
Back to Newton’s Second Law
3
Impulse-Momentum
Theorem
What is this theorem?
Average force
4
Example – Momentum and
Impulse
A 50-g golf ball is struck with
a club as shown. The force on
the ball varies from zero when
contact is made up to some
maximum value (when the
ball is deformed) and then
back to zero when the ball
leaves the club. The forcetime graph is also shown.
Assume the ball leaves the
club face with a velocity of
+44m/s
1.
1.
2.
Estimate the size and
direction of the impulse due to
the collision.
Estimate the duration of the
collision and the average force
on the ball.
5
Injury in Car Collision
Data:
Survival data for head on
collision: Force for bone
fracture 90KN, Pressure
1.9x105N/m2 at 60 mi/h
resulting in acceleration
of 50g’s for 70 ms for
an area of 0.7-0.9 m2
Case Data Mp = 75-kg, Vi
=60 mi/h (27m/s),
tr=0.010 s,
Achest+head=0.5 m2
Find F, a, P
6
Air Bags and Seat Belts
The air bag increases
the time of the
collision
It will also absorb
some of the energy
from the body
It will spread out the
area of contact
decreases the
pressure
helps prevent
penetration wounds
7
Conservation of
Momentum
What is this conservation law?
What do we mean by a system?
What do we mean by an isolated
system?
Is contact necessary?
Another way to say the same thing
8
Conservation of
Momentum
Is contact
necessary?
Another way to
write conservation
of momentum
9
Types of Collisions
What is Inelastic
collision?
What is Elastic
collision?
10
Example – Inelastic Collision
1.
A bullet of mass m with a speed v into a
wooden block of mass M. Find an
expression that gives the initial velocity of
the bullet in terms of masses, acceleration
due to gravity g and the height h thru
which the pendulum is raised.
11
Example – Elastic Collision
1.
A bullet of mass m and
speed v passes
completely through a
pendulum bob of mass M.
The bullet emerges with a
speed v/2. The pendulum
bob is suspended by a
stiff rod of length l and
negligible mass. What is
the minimum value of v
such that the pendulum
bob will barely swing
through a complete
vertical circle? (Find the
expression in terms M, m
g and l).
12
Glancing Collisions
13
Example – Glancing Collision
1.
A 1500kg car traveling
east with a speed of 25
m/s collides at an
intersection with a
2500kg van traveling
north at a speed of 20
m/s as shown. Find the
direction and magnitude
of the velocity of the
wreckage after the
collision, assuming that
the vehicles undergo a
perfectly inelastic
collision (that is, they
stick together) and
assuming that friction
between the vehicles
and the road can be
neglected.
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