Newton’s Three Laws and Momentum and Concepts

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Newtons Three Laws and Momentum and Concepts
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Newtons 1st Law

• A body in motion (or at rest) tends to stay in
  motion (or at rest) if no forces acts upon it
• In momentum concepts this becomes an object has
  momentum

2 pts on test
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Momentum

• The symbol for momentum p
• The units for momentum kgm/s
• Momentum is a vector and therefore has direction.
  An object that is traveling north has a different
  momentum than a vector traveling south

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The formula for momentum p m x v, RV versus
Mini

• i. The RV would have a bigger momentum because it
  has more mass
• ii. The RV would be more likely to stay in motion
  because it has a bigger momentum from its bigger
  mass.
• iii. The RV would have a harder time stopping
  because it has a bigger momentum from its bigger
  mass.
• iv. The RV would do more damage if it hit
  anything, with its large mass, because it has a
  bigger momentum from its bigger mass.

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The formula for momentum p m x v, Volvo at
100mi/hr vs Volvo at 50 mi/hr

• i. The 100 mi/hr-Volvo would have a bigger
  momentum because it has more speed
• ii. The 100 mi/hr-Volvo would be more likely to
  stay in motion because it has a bigger momentum
  from its bigger speed.
• iii. The 100 mi/hr-Volvo would have a harder time
  stopping because it has a bigger momentum from
  its bigger speed.
• iv. The 100 mi/hr-Volvo would do more damage if
  it hit anything, with its large mass, because it
  has a bigger momentum from its bigger speed.

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Newtons 2nd Law

• Fma
• In momentum concepts this becomes
• J Ft ?p
• (called the impulse-momentum theory)
• (you do NOT need to know the derivation, but it
  comes from
• a ?v / t, and m?v?p)
• The symbol for impulse is J, with the units
  Nsec
• Impulse is a vector, therefore it has direction

2 pts on test
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Impulse

• Example A) a mack truck would have a greater
  impulse simply because it has more momentum than
  a compact car
• Example B) the volvo going 100 mi/hr would have a
  greater impulse than the other volvo going 30
  mi/hr because it too has a greater momentum

• Didn't talk about Concept Problems 4-6 about
  pitched vs caught (same impulse since same Dv for
  each, but caught bigger force since t smaller
  in Ft mDv), or bullets from pistols vs rifles
  (rifle bigger Dv since bigger t in FtmDv). ?

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Impact timelong vs. short

• The shorter the impact time the larger the force
  (WHY???)
• needed to say Use the equation JFt where J is
  constant
• Example Lets compare a karate chop from a bunt
  of a baseball. A karate chop occurs during a
  small time period and creates a strong force.
  Thinking oppositely, when you want to bunt a
  baseball, you take a swing for a period of time,
  making a small force so the ball wont go to the
  other team.

• For bunting, should have said move bat backwards
  to increase impact time so force on ball is
  lessened. MANY other examples! ... such as
  Concept problems 7 or 8 (landing when jumping, or
  catching a hardball bare-handed.)

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Bouncing vs. Sticking in Collisions

• Lets compare two objects, one that bounces and
  one that sticks. An object that bounces will have
  a bigger velocity when it hits the ground and
  therefore a bigger momentum and a bigger force
  and bigger impact time than an object that would
  stick to the floor. This is because when an
  object bounces off the floor the final velocity
  is negative, meaning that it has a large change
  in momentum
• Object that bounces has a bigger ?v, ?p, F, and J

? The part in purple is WRONG. There is a
difference between velocity and change in
velocity they are NOT the same thing! (Note
if we werent so lazy it would be called the
impulse-change in momentum formula, because it
is CHANGE that is in that formula! On the test,
make up numbers of a specific example Bounce v0
100 m/s, vF -100 m/s, so ?v (-) 200
m/s Stick v0 100 m/s, vF 0 m/s, so ?v
(-)100 m/s Its the CHANGE in VELOCITY that is
greater, so the 2nd bullet above is correct
bounces has a bigger ?v, ?p, F, and J BUT, didnt
talk about any specific examples in Concept
Problems 9-12 (bullets, cars, etc)
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Impulse Momentum Problems

• When finding the change in momentum we use this
  formula
• JFt?ppf-pimvfm(Vf-Vi)m?v
• a b c d e f
  g

• Only J and F should be capitals all others are
  lower case. The f and i for final and initial
  should be subscripted!
• Memorize at least first 3 parts for test!

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Impulse Momentum Problems

• Example Rocio strikes a 0.058-kg golf ball with a
  force of 272 N and gives it a velocity of 62.0
  m/s. How long was Rocios club in contact with
  the club?
• M0.058-kg
• F272N
• V62.0 m/s
• Use F x t m x v
• (272N)(t)(0.058kg)((62.0m/s)
• t0.013 sec

• This is wrong. If you look at the last slide,
  that formula has CHANGE IN velocity, not
  velocity.
• How could/should this problem be fixed? Hint v0?

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Impulse Momentum Problems

• Example A Force of 186 N acts on a 7.3-kg bowling
  ball for 4.0 s. What is the bowling balls change
  in momentum? What is the bowling balls change in
  velocity?
• F 186N
• m 7.3 kg
• t 4.0 sec
• ? p ?
• For finding momentum use F x t ? p
• So (186N)(4.0sec) ? p
• ?p 744 kgm/s
• For finding velocity use F x t m x v
• (186N)(4.0sec) (7.3-kg)(v)
• v 102. m/s

• How could/should this problem be fixed? (There
  are 3 of the 4 purple things that are wrong.)

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Newtons Third Law

• When one object exerts a force on another, the
  second exerts a force of equal magnitude on the
  first, but in the opposite direction
• In momentum concepts this becomes momentum is
  conserved in a closed and isolated system
• When a system is closed or isolated, ?Fon the
  system 0, and thus Jon the system 0, so ?pof
  the system 0 too.
• (Recall J Ft ?p)
• In other words P initial total P final total

2 pts on test

• P should be a lower case p. Remember to write
  ppinitial total pfinal total for EACH cons. of
  momentum problem on the test!

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Conserved vs Constant

• Conserved total amount before and after is the
  same, but the forces can transfer
• Constant there is no change
• While constant and conserved may seem the same,
  there are some differences a constant system has
  objects that never change at all a conserved
  force overall does not change over a time period,
  but the internal forces transfer
• Closed nothing enters or leaves a system
• Isolated no external forces (no friction)

• Excellent defn. BUT, forces do not transfer.
  MOMENTUM TRANSFERS.
• Better to say there is no change in any objects
  momentum at all, ever.
• Constant is done OK, but once again forces are
  being confused with conserved momentum
• 4 points on the test to know the 2 conditions
  required for the conservation of momentum and to
  define each of them separately.
• PS know that in science, energy and mass are
  also conserved quantities
• ? Didn't talk about Concept Problems 26-27, or
  16-21.

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The Recoil Effect

• Recoil effect can be explained in two different
  ways
• (A) equal but opposite forces
• or (B) the conservation or momentum....
• pit0
• then if pFa20 kgm/s, pFb ?20 kgm/s
• therefore pFt0
• And finally, pitpFt

• Didnt give any specific examples from Concept
  Problems 22-25 (or lab or cat or hose, etc) and
  didnt explain with method A well enough. They
  would get full credit for method B. 8 points on
  unit test!!!!!!

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Conservation of Momentum Problems

• Example Two lab carts are pushed together with a
  spring mechanism compressed between them. Upon
  release, the 5.0-kg cart repels one way with a
  velocity of 0.12 m/s, while the 2.0-kg cart goes
  in the opposite direction. What is the velocity
  of the 2.0-kg cart?
• PitPFt
• (5-kg)(0) (2.0-kg)(0) (5-kg)(0.12m/s)
  (2.0-kg)(VF)
• Vf -0.30 m/s

• P and V should be a lower case p and v.
• BE VERY CAREFUL OF DIRECTION IN THESE and JFt
  problems bounces, head-on, hit back are
  all words to mean one of the velocities will be
  negative!

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Take this self-QUIZ

• Write EACH of Newtons 3 laws (in order), and
  what they become in our Momentum unit
• If a thrust of 35 Newtons is used to change the
  velocity of a 72000-kg craft by 0.63 m/s. How
  long should the thrusters be applied?
• A 0.115-kg hockey puck moving 35.0 m/s strikes an
  octopus sitting on the ice. The octopus has a
  mass of 0.265 kg. Find their velocity as they
  slide off together.
• Can you explain recoil effect with both Ns 3rd
  law and momentum concepts??
• Can you explain impact time??
• What about bouncing vs sticking?
• Do you know how to do a 2-dimensional problem??
• Do you know at least 6 correct things about
  angular momentum??