Momentum & Impulse
Pg. 222- 227
Momentum & Impulse
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The driver of this race car
walked away from the car
without a scratch
Luck had little to do with
this fortunate outcome
though – a practical
application of Newton’s
laws of motion by the
engineers who designed
the car and its safety
equipment protected the
driver from injury
Momentum
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When Newton originally formulated his laws of motion,
he expressed them in a somewhat different form than
you can see in most textbooks today.
Newton emphasized a concept called a “quantity of
motion”, which is defined as the product of an object’s
mass and its velocity.
Today, we call this quantity “momentum”
Momentum
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Since momentum is the product of a vector and a scalar,
momentum is a vector quantity
The direction of the momentum is the same as the
direction of the velocity
note
Momentum (p)
Practice
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1. Determine the momentum of a 0.30 kg hockey puck
travelling across the ice at a velocity of 5.6 m/s [N]. (1.7 kg-m/s)
Impulse
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Newton’s first law states that the
velocity of an object is constant
unless acted on by an external force
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So, if a net force is applied to an
object, its velocity will change and,
therefore, its momentum will also
change
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Expressed mathematically, his second
law, F=ma, can be rewritten as:
note
Impulse (∆p)
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2. If a golf club exerts an average force of 5300 N[W] on
a golf ball over a time interval of 0.00054 s, what is the
impulse of the interaction?
Impulse-Momentum Thery
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In many collisions, It is exceedingly difficult to make the
precise impulse
This is because the force changes continually throughout
few milliseconds of contact between the two object
Impulse-Momentum Theory
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For example, when a golf club first contacts a golf ball, the
force is very small
Within milliseconds, the force is great enough to deform
the ball
The ball then begins to move and return to its original
shape and the force soon drops back to zero
Impulse-Momentum Theory
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You could find the impulse by determining the area under
the curve of force versus time (which can be tedious)
An alternative and much easier approach is to analyze the
momentum before and after the interaction between two
objects
Impulse-Momentum Theorem
note
Practice
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3. A 0.16 kg puck is traveling at 5.0 m/s[N] when a slapshot
changes the puck’s velocity to 40 m/s[S]
If the collision lasted 0.0020 s,
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A) calculate the impulse imparted by the hockey stick
B) determine the average force applied by the stick to the puck
4. A student practices her tennis volleys by hitting a ball
against a wall
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A) if the 0.060 kg ball travels at 50 m/s[W] before hitting the wall
and then bounces directly backward at 35 m/s[E], what is the impulse
of the interaction?
B) if the duration of the interaction is 25 ms, what is the average
force exerted on the ball by the wall?
Impulse & Auto Safety
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Once of the most practical and important applications of impulse is
in the design of automobiles and their safety equipment
When a car hits another car or a solid wall, little can be done to
reduce the change in momentum
The mass of the car certainly does not change, while the velocity
changes to zero at the moment of impact
Since you cannot reduce the change in momentum, you cannot
reduce the impulse
However, since impulse (F∆t) depends on both force and time,
engineers have found ways to reduce the force exerted on car
occupants by extending the time interval of the crash
Impulse & Auto Safety
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In the early days, engineers and designers thought that a very strong,
solid car would be ideal
As the number of cars on the road and the speed of the cars
increased, the number and seriousness of accident injuries made it
clear that the very sturdy cars were not protecting the car
occupants
By the late 1950s and the early 1960s, engineers were designing cars
with very rigid passenger cells that would not collapse on the
passengers, but with less rigid “crumple zones” in the front and rear,
as shown
Impulse & Auto Safety
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When a rigid car hits a wall, a huge force stops the car
almost instantaneously
The car might even look as though it was only slightly
damaged
However, parts of the car, such as the steering wheel,
windshield, or dashboard, exert an equally large force on
the passengers, stopping them exceedingly rapidly and
possibly causing very serious injuries
Impulse & Auto Safety
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When a car with well-designed crumple zones hits a wall,
the force of the wall on the car causes the front of the
car to collapse over a slightly longer time interval than it
would in the absence of a crumple zone
Since F∆t is constant and ∆t is larger, the average force, F,
is smaller than it would be for a rigid car
Although many other factors must be considered to
reduce injury in collisions, the presence of crumple zones
has had a significant effect in reducing the severity of
injuries in automobile accidents
Impulse & Safety Equipment
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The concept of increasing the duration of an impact applies to
many forms of safety equipment
For example, the linings of safety helmets are designed to
compress relatively slowly
If the lining was extremely soft, it would compress so rapidly
that the hard outer layer of the helmet would impact on the
head very quickly
If the lining did not compress at all, it would collide with the
head over an extremely short time interval and cause serious
injury
Each type of sport helmet is designed to compress in a way
that compensates for the type of impacts expected in that
sport
note
Impulse & Safety
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Since ∆p = F∆t and ∆p does not change when time is
increased in order to decrease force
Important application is in the design of safety equipment
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Crumple zones
Air bags
Safety helmets
Sports equipment
(although a car crash seems almost instantaneous, the time
taken for the front or rear of the car to “crumple” is great
enough to significantly reduce the average force of the impact
and, therefore, the average force exerted on the passenger cell
and the passengers)
Practice
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5. A bungee jumper jumps from a very high tower with
bungee cords attached to his ankles. As he reaches the
end of the bungee cord, it begins to stretch. The cord
stretches for a relatively long period of time and then it
recoils, pulling him back up. After several bounces, he
dangles unhurt from the bungee cord. Use the concept
of impulse to explain the different in the results of a jump
using a proper bungee cord and a jump using an ordinary
rope.
Textbook
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Pg. 227 #3,5, 9 -11
Pg. 257 #1-4 (PJ: Momentum & The Neutrino)