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Momentum – Impulse
Collisions
• Momentum
Inertia  Objects at rest or Objects in motion
The concept of inertia in motion is called Momentum
Which one is harder to stop? A large truck or a small car?
momentum = mass x velocity
momentum = m ∙ v
• Impulse Changes Momentum
If momentum changes  mass, velocity or both change
If velocity changes  We have acceleration
What causes acceleration?  Force
The greater the Force acting on an object  the greater its change in
velocity  the greater its change in momentum
How long this force acts, it is also important.
The quantity of force x time interval is called impulse
impulse = F ∙ t
impulse = change in momentum  F ∙ t = m ∙ v
F∙t =m∙v
Review Questions
•
Distinguish between mass and momentum. Which is inertia and which is inertia in
motion?
•
Which has the greater mass, a heavy truck at rest or a rolling skateboard?
Which has the greater momentum?
•
When the force of impact on an object is extended in time, does the impulse
increase or decrease?
•
Does impulse equal momentum or a change in momentum?
•
In a car crash, why is it advantegeous for an occupant to extend the time during
which the collition takes place?
•
If the time of impact in a collision is extended by four times, how much does the
force of impact change?
•
Why is it advantageous for a boxer to ride with the punch? Why should he avoid
moving into an oncoming punch?
• Bouncing
Impulses are greater when an object bounces.
The impulse to bring an object to stop and then to “throw it back
again” is greater than the impulse required merely to bring the
object to a stop.
Pelton Wheel
Curved blades
prolong contact
with water:
Impulse = F Dt
Greater impulse
means greater
change in
momentum of
the wheel.
• Conservation of Momentum
Newton’s second Law: To accelerate an object, a net force must
be applied on it
To change the momentum of an object, exert an impulse on it.
Momentum
Before = 0
------------Momentum
After = 0
------------After firing,
the opposite
momenta
cancel.
In the absence of an external force, the momentum of a system remains
unchanged.
momentum (before) = momentum (after)
• Collisions
In the absence of external forces, the net momentum of both objects
before collision, equal the net momentum of both objects after
collision
net momentum (before collision) = net momentum (after collision)
Elastic Collisions: When objects collide without being permanently
deformed and without generating heat, the collision is said to be an
elastic collision
Inelastic Collisions: Momentum conservation holds true even
when colliding objects become distorded and generate heat during
collision. Whenever colliding objects become tangled or coupled
together, a totally inelastic collision occurs.
net momentum (before collision) = net momentum (after collision)
net m ∙ v (before) = net m ∙ v (after)
Diesel: m = 8000 kg, v = 5 km/h
/ Wagon: m = 2000kg, v = 0 km/h
8000 kg ∙ 5 km/h + 2000 kg ∙0 km/h = 10,000 kg ∙ 4 km/h
Elastic Collisions:
net momentum (before collision) = net momentum (after collision)
Car "Rear-Ends" Truck - Elastic
Truck "Rear-Ends" Car - Elastic
Inelastic Collisions:
net momentum (before collision) = net momentum (after collision)
Car "Rear-Ends" Truck - Inelastic
Truck "Rear-Ends" Car - Inelastic
Problem Solving:
Consider a 8 kg fish that swims toward and swallows a 2 kg fish that
is at rest. If the larger fish swims at 5 km/h, what is the velocity
immediately after lunch?
net momentum (before collision) = net momentum (after collision)
• Momentum Vectors
Momentum is conserved even when interacting objects don’t move
along the same straight line.
Momentum, like the quantities velocity and force, has both direction
and magnitude. It is a vector quantity.
net momentum (before collision) = net momentum (after collision)
Review Questions
•
Why is more impulse delivered during a collision when bouncing occurs than
during one when it doesn’t?
•
Why is the Pelton Wheel an improvement over paddle wheels with flat blades?
•
In terms of momentum conservation, why does a cannon recoil when fired?
•
What does it mean to say that momentum is conserved?
•
Distinguish between an elastic and an inelastic collision.
•
Imagine that you are hovering next to the space shuttle in an Earth orbit. Your
buddy of equal mass, who is moving at 4 km/h with respect to the shuttle, bumps
into you. If he holds onto you, how fast do you both move with respect to the ship?