LESSON 1.12 - MOMENTUM
Overview
This lesson deals with
impulses and momentum. On completion of the lesson, you
should be able to determine the momentum of a moving
object. You should also be able to describe the effect of
time in the transfer of momentum and how more momentum is
transferred when bouncing occurs.
ACTIVITIES
- Hammer and nail: Use
two different hammers with different sized heads
to drive a nail into a piece of wood. Show how
the momentum of the hammer affects the way that
the nail is driven.
- Roll a small marble
along a table so that it collides with a larger
marble. Roll the larger marble at a similar speed
so that it collides with the smaller marble.
Observe the transfer of momentum during the
collisions
Newton’s Second
Law
Newton’s Second Law states that a force is needed to
cause acceleration.
Impulse
An impulse is a force applied for a particular period of
time. Impulse is the product of force and time. The SI
unit of impulse is the Newton-second. (N-s)
An impulse is needed to change the momentum of an object.
The force used to change
the momentum of an object can vary according to the time
taken. To catch an egg, it is advisable to use as much
time as possible to slow the egg down. This keeps the
amount of force needed to a minimum and may prevent
breaking the egg.
Bouncing
Would you prefer to be hit by a water balloon with 200 g
of water in it or by a tennis ball with 200 g of water in
it traveling at the same speed as the water balloon? The
encounter with the water balloon would be less painful
because it would not bounce on impact. When an object
bounces, it changes direction completely and moves off in
the opposite direction at a relatively high speed. A
bouncing object transfers much more momentum during
impact because it has momentum in the opposite direction
after impact. Because momentum needs to be conserved in
each direction, the momentum of the target after
collision must be greater to account for the opposite
momentum of the bouncing object.
Example 1.12.1 Momentum
What is the momentum of a
truck with a mass of 1,200 kg moving at 3 m/s?
Solution
Momentum = mv = 1,200 x 3
= 3,600 N-m
Example 1.12.2 Impulse
A force of 5 N is applied
for a period of 0.06 seconds to a projectile with a mass
of 0.5 kg.
By how much does the
velocity of the projectile increase?
Solution
The impulse = 5 x 0.06 = 0.3
N-s.
This equals the change in
momentum, which equals 0.5 x the change in velocity.
The change in velocity
= 0.3 / 0.5 = 0.6 m/s
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Review
Questions
- Which has the greater
momentum: A train that is stopped at a railway
station or an ant walking along a table top?
- Which has the greater
momentum: A bullet with a mass of 40 grams
traveling at 300 m/s or a cannon ball with a mass
of 5 kg traveling at 20 m/s?
- Why does a bullet
fired from a rifle travel further than the same
type of bullet fired from a revolver?
- Why can an archer
shoot an arrow further using a compound bow than
with a conventional bow?
- One golfer hits a
ball with an average force of 100 N with the club
in contact with the ball for 0.05 seconds.
Another golfer hits the ball with an average
force of 150 N and the ball remains in contact
with the club for 0.043 seconds. Which ball will
travel further? Why?
- Why are air bags
better than seat belts in preventing injuries
during collisions?
- A bowling ball with a
mass of 2.5 kg rolls along a smooth wooden floor
at a velocity of 4 m/s. Will more momentum be
transferred if it hits a wall and bounces back or
if it hits a second ball and stops as a result of
the collision?
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ACTIVITIES
- Hammer and nail: Use
two different hammers with different sized heads
to drive a nail into a piece of wood. Show how
the momentum of the hammer affects the way that
the nail is driven.
- Roll a small marble
along a table so that it collides with a larger
marble. Roll the larger marble at a similar speed
so that it collides with the smaller marble.
Observe the transfer of momentum during the
collisions
.
.
HANDS-ON
HOMEWORK
Select one or more of the recommended
activities for Lesson 1.13, collect the items needed and test the
procedure before demonstrating the activity during the
next theory lesson.
Lesson
1.12 Momentum
- The ant.
- Momentum of bullet =
0.04kg x 300 m/s = 12 kg-m/s
Momentum of cannon ball = 5kg x 20 m/s = 100 kg-m/s
The cannon ball has the greater momentum.
- The longer barrel
enables the high-pressure gasses that propel the
bullet to exert a force on the bullet for a
longer period of time. The impulse provided is
therefore greater.
- The force applied by
a compound bow is more even over the time that
the arrow is in contact with the string. The
impulse is greater.
- The impulse from the
club of Golfer 1 = 100N x 0.05s = 5 N-s
The impulse from the club of Golfer 2 = 150N x 0.043s
= 6.45 N-s.
The second golfer should hit the ball further.
- Seat belts absorb the
force of impact over a much shorter time than air
bags. For the same impulse, the force is much
greater.
- The ball transfers
more momentum in its original direction if it
needs to reverse its direction.
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