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"Momentum", "Conservation of Momentum", and "Collisions: Elastic & Inelastic"
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Think about a soccer player kicking a moving ball during a game. At the moment that he kicks the ball, the ball's velocity changes rapidly and the direction changes too.
How can the changing motion of the ball when struck be explained?
Force and Newton's laws can be used to explain why the motion of the ball changes when struck.
What is momentum?
Momentum is defined as the product of the object's mass and it's velocity.
What is the equation for momentum?
Momentum is represented by {p}
p = m × v
What are the SI units for momentum?
SI units: kg m/s
A class takes a field trip to the bowling alley. Student 1 gets a bowling ball with a mass of 4.5kg and rolls it with a velocity of 6.6 m/s. Student 2 picks up another bowling ball of the same mass and rolls it with a velocity of 4.2 m/s.
Which ball has more momentum?
Ball 1: 4.5 kg × 6.6 m/s = 29.7 kg m/s
Ball 2: 4.5 kg × 4.2 m/s = 18.9 kg m/s
The first ball has more momentum.
I am driving a truck with a mass of 907 kg going 80 km/hr and Jake is driving a 2 door coupe with a mass of 454 kg driving 150 km/hr.
Which driver has more momentum?
The truck has more momentum
What can we see in both the bowling ball and truck example?
In these examples, we can see a relationship between momentum and force.
How did Newton first express his second law of motion?
Newton first expressed his second law of motion as
F = ∆p/∆t = change in momentum/time interval
How did Newton eventually express his second law of motion?
He wrote it as F = m × a
How can the equation for momentum be rearranged to find the change in momentum in terms of the net external force and the time interval required to make this change?
F∆t = ∆p
or
F∆t = ∆p = mv(sub. f) - mv(sub. i)
How will we consider all forces exerted on an object?
We will consider all forces exerted on an object are assumed to be constant.
What is the impulse-momentum theorem?
The expression F∆t = ∆p is called the impulse-momentum theorem.
What does the equation F∆t explain?
F∆t = ∆p explains why follow through is important.
What does the extension of the time interval over which a constant force is applied allow for?
Extending the time interval allows for a smaller force to cause a greater change in momentum.
Who else uses the impulse momentum theorem?
Highway safety engineers use the impulse momentum theorem to determine stopping distances and safe following distances for vehicles.
How else is the impulse momentum theorem used?
It is also used to design safety equipment that reduces the force exerted on the human body.
According to the conservation of momentum, what can be said of the momentum of the solid ball and white ball?
According to the conservation of momentum, the amount of momentum the solid ball gains is exactly equal to the momentum the white ball loses.
How does the total momentum of the two balls together change?
The total momentum of the two balls together remain constant.
What is the equation for Conservation of Momentum?
p(sub. ai) + p(sub. bi) = p(sub. af) + p(sub. bf)
What is the law of conservation of momentum?
The relationship—the total momentum of the two balls together remain constant—is true for all interactions between isolated objects is known as the law of conservation of momentum.
What is the total momentum of all objects interacting with one another?
The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects.
How does Newton's third law lead to the conservation of momentum.?
Because impulse is equal to the change in momentum and the impulse on m₁ is equal to and opposite the impulse on m₂, the change in momentum of m₁ is equal to and opposite to the change in momentum of m₂.
What is the momentum of every interaction between two isolated objects?
The change in momentum of the 1st object is equal to and opposite to the change in momentum of the 2nd object.
∆p = -∆p₂
What should be used when solving impulse problems?
When solving impulse problems, you should use the average force during the collision as the value for force.
Regardless of the type of collision, what is the total momentum?
Regardless of the type of collision, the total momentum remains constant.
Regardless of the type of collision, what is the total kinetic energy?
However, the total kinetic energy is generally not conserved in a collision because some kinetic energy is converted to internal energy when objects deform.
What are the two extreme types of collisions we will focus on?
We will focus on two extreme types of collisions:
elastic & perfectly inelastic.
What is a perfectly inelastic collision?
When 2 objects collide and move together as one mass, the collision is called perfectly inelastic, such as an arrow and target.
Why are elastic & perfectly inelastic collision easy to analyze in terms of momentum?
These types of collisions are easy to analyze in terms of momentum because the objects become essentially one object after collision.
What is the final mass of two colliding objects in a perfectly inelastic collision?
The final mass is equal to the combined masses of the two objects and they move with the same velocity after colliding.
What is the equation for a perfectly inelastic collision?
m₁v1₁(sub. i) + m₂v₂(sub. i) = (m₁ + m₂)v(sub. f)
In an inelastic collision, what is the total kinetic energy?
The total kinetic energy does not remain constant when objects collide and stick together.
Some kinetic energy is converted to in an inelastic collision?
Some kinetic energy is converted to sound energy and internal energy as the objects deform during collision.
What is the result of two colliding objects in an elastic collision?
In an elastic collision, two objects collide and return to their original shapes with no change in total kinetic energy.
What is the total momentum and total kinetic energy in an elastic collision?
In an elastic collision, both the total momentum and total kinetic energy remain constant throughout the collision.
What does the production of sound indicate?
Any collision that produces sound is not perfectly elastic, the sound representing a decrease in kinetic energy.
What category does most collisions actually fall into?
Most collisions actually fall into a category inelastic collisions
What is an inelastic collision?
In an inelastic collision, the colliding objects bounce and move separately after the collision but the total kinetic energy decreases in the collision.
What is the total momentum and the total kinetic energy in all collisions?
We will assume that the total momentum and the total kinetic energy remain constant in all collisions.
What is the law of conservation of momentum?
Momentum is concealed
What two factors affect momentum?
Mass and velocity
What are the units for p?
kg × m/s
p is momentum
What is the expression for impulse?
Ft
Name the three types of collisions.
Elastic, inelastic, and perfectly inelastic
What are the units for impulse?
N × s
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