Transcript Momentum

“inertia in motion”
Which is harder to stop?
momentum = mass x velocity
Both can have large momenta:
Example 6.1
A 100kg football player runs with a
velocity of 4.0 m/s straight down the field.
A 1.0kg artillery shell leaves the barrel of
a gun with muzzle velocity of 500 m/s.
Which has the greater momentum
(magnitude), the football player or the
shell?
 pf = 400 kg m/s, ps = 500 kg m/s
So the less massive shell has greater
momentum!

How do you change momentum?
If the momentum of an object changes,
either the mass changes or the velocity
changes.
 Most often it’s the velocity that changes,
which means there is an acceleration,
which means there must be a net external
force!
 The greater the force, the greater the
change in velocity, and then the greater
the change in momentum!

But TIME is also important!
Newton’s Second Law
F = ma = m (Δv/ Δt)
F Δt = m Δv = Δ(mv)
F Δt = Δp
“Impulse” = change in momentum
Important point regarding ∆p

The figure below shows a ball bouncing off
a wall. What is the ball’s change in
momentum during the bounce? What is
the direction of the average force on the
ball as it bounces?
Increasing momentum
Which would you pick?
Decrease momentum
over a long time
Why does the egg not break
when it hits the sheet?
Example 6.4
A golfer drives a 0.046-kg ball from an
elevated tee, giving the ball an initial
horizontal speed of 40 m/s (about 90
mph). What is the magnitude of the
average force exerted by the club on the
ball during this time?
 1800N
 Follow-up: what if the golfer “follows
through” with the same force for 1.5ms
more time? How will velocity change?

Example 6.5
A 70.0-kg worker jumps stiff-legged from
a height of 1.00m onto a concrete floor.
 (a) What is the magnitude of the impulse
he feels on landing, assuming a sudden
stop in 8.00 ms?
 (b)What is the average force?
 (a) 310 kg m/s (b) 38,800 N (~8730lbs)

Momentum over short time
Impulses are greater when bouncing
takes place.
Conservation of momentum
If you wish to accelerate an object, you
must apply a force to it. (Newton’s
second law)
If you want to change the momentum of
an object, you must exert an impulse
on it.
Basically the same thing!
Force or impulse must be exerted on the
object by something outside the object.
Internal forces do not count!
Net momentum here is still zero!
Momentum is a vector quantity!
+
=0
If no net force acts on a system, then the
momentum of that system cannot change.
No net external force!
Law of conservation of momentum
In the absence of an
external force, the
momentum of a
system remains
unchanged.
Formulas
Momentum:
p = mv
Impulse:
F Δt = Δp