Lecture 6, Linear Kinetics - Momentum and Impulses

Question 1

Understanding Forces

Answer 1

Sir Isaac Newton (1643-1727)
- physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian
Newton’s Apple
- “why should that apple always descend perpendicularly to the ground, thought he to himself. why should it not go sideways or upwards, but constantly to the earth’s center?”
Philosophiæ Naturalis Principia Mathematica (1687)
- laid the foundation for classical mechanics

my notes:
- forms the basis for movement
- these are now laws and no longer theories as they have been proven
- explain why things happen - would take what other people had seen and combine it with his observations

Question 2

Newton’s First Law

Answer 2

newton said:
“every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed”
law of inertia
- everybody remains in a state of constant velocity
◦ the system remains at rest
◦ the system moves in a uniform
manner
- unless acted upon by an external force
- we have a desire to remain in a static state and do whatever it is we are doing as it easy and does not require any more energy (velocity is constant) - we need a force to change the state of motion
- inertia means the resistance to change
- continue doing what it is you are doing unless a force is exerted on you - you will continue to move in constant motion unless external force is create by you or someone else

Question 3

Inertia

Answer 3

a tendency to remain unchanged
- the amount of inertia in a system is proportional to its mass
- mass = quantity of matter (in kilograms) contained in an object
- how much inertia you have is dependent - the bigger you are the more inertia you have - big mass more inertia (more force to create changes) and small mass = small interia
- a heavier object would be more resistant to change
- a lighter object would be easier to change

Question 4

Momentum and Newton’s First Law

Answer 4

• when an object is in motion, it has momentum
• momentum is the quantity of motion (for an object to have momentum it needs to be moving)
  the property that a moving object has due to its mass and its motion
• the strength or force that something has when it is moving
  momentum = mass x velocity
  M = mv
  units: kg m/s
• momentum looks at the consequence of motion as you are moving you can apply movement to other objects
• the bigger you are or the faster you are moving the more you can affect and more momentum you can create
• momentum takes into account system (mass - big or small) and velocity (the bigger the mass the more the affect)
• the effect a moving system will have - the more movement you can create

Question 5

Momentum and Newton’s First Law (continued)

Answer 5

• according to Newton’s First Law, in the absence of an external force every system remains in a constant state
• so, the momentum in one instance should be the same as the momentum in another instance
  ◦ M1 = M2
  ◦ conservation of momentum
• whatever you are doing in one instance is not going to change in another (in rigid-body you do not change) - mass is never changing
• the conservation of momentum (it is about velocity not mass) - if velocity is not changing then momentum is not changing

Question 6

The Conversation of Momentum

Answer 6

the momentum (velocity) of the stick is transferred to the puck
- you have an affect on something else (give it some of your movement so you lose a bit but it is transferred)
- the stick may lose some velocity but it is not breaking because rigid body
gives its velocity to puck
- player can speed up and heavier stick (maximize momentum) - what is the heaviest stick i can have without losing too much velocity
- use lighter equipment (to increase in limb velocity)
- use heavier equipment (to increase mass

Question 7

Newton’s Second Law

Answer 7

newton said:
- “the rate of change of momentum of a body (or the acceleration for a body of constant mass) is proportional to the force causing it and the change takes place in the direction in which the force acts.”
Newton’s Second Law is The Law of Momentum
- in order to change the momentum of a system, we need to apply a force over a period of time
- is the desire to change the state to be in a dynamic state - going to change the momentum of a system where a force is applied over a period of time
- forced applied against a system is going to change the momentum of the system
- it is not about calculating momentum it is about CHANGING momentum and in order to change you need a force applied over a period of time to change the momentum (ON QUIZ)

Question 8

Impulse and Newton’s Second Law

Answer 8

• the amount of change is proportional to the magnitude of the force and the time during which it acts
• a change in momentum is produced by an impulse
  ◦ impulse = force x time
  ◦ impulse = Ft
  ◦ units: Ns
• force applied over a period of time is an impulse
• impulse changes momentum
• whatever your momentum is one in instance will be different the next time
• impulse = Ft
• impulse = change in momentum
• change in momentum = m2 - m1
• change in momentum = mv2 - mv1 (mass is not changing - rigid-body mechanics) the changing factor is velocity which is defined by force

Question 9

Newton’s Second Law Re-Examined

Answer 9

Newton’s Second Law is The Law of Momentum
- “the rate of change of momentum of a body (or the acceleration for a body of constant mass) is proportional to the force causing it and the change takes place in the direction in which the force acts.”

however, often referred to (incorrectly) as the Law of Acceleration
- a force applied to a body causes an acceleration of that body of a magnitude proportional to the force, in the direction of the force, and inversely proportional to the body’s mass
- it is both law of acceleration and law of momentum (say the exact same thing)
- do not memorize what he said just the principle behind it
- force applied to a mass causes acceleration

Question 10

Newton’s Second Law Re-Examined

Answer 10

why is Newton’s Second Law referred to as the Law of Momentum and the Law of Acceleration? (TEST)
- given as a formula and then you explain it on a test
- the law of momentum Ft = mv2 - mv1 (the time period is irrelevant what matters is the force and how it changes the system)
- F = mv2 - mv1 / t
- F = m (v2 - v1) / t (a force qpplied to a system is going to change velocity overtime which then means acceleration)
- F = ma
- a force applied to a system accelerates it which is change in velocity with respect to time

Question 11

Newton’s Third Law

Answer 11

newton said:
- “if a body impinges upon another, and by its force changes the motion of the other, that body also will undergo an equal change, in its own motion, toward the contrary part.”
The Law of Action and Reaction
- for every force applied by one body on a second, the second body applies an equal and oppositely directed force on the first
- the reaction or contact force acts on a system
◦ the reaction or contact force can generate movement
- there are consequences to your reaction as there are equal and opposite reactions (if you push down on a desk it pushes back equally)
- reactions forces we need to create full body movement