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Newton’s Three Laws and Momentum and Concepts

Newton’s Three Laws and Momentum and Concepts. Newton’s 1 st 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. Momentum. The symbol for momentum: p

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Newton’s Three Laws and Momentum and Concepts

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  1. Newton’s Three Laws and Momentum and Concepts

  2. Newton’s 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

  3. Momentum • The symbol for momentum: p • The units for momentum: [kg*m/s] • Momentum is a vector and therefore has direction. An object that is traveling north has a different momentum than a vector traveling south

  4. 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.

  5. 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.

  6. Newton’s 2nd Law • F=ma • 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 [N*sec] • Impulse is a vector, therefore it has direction 2 pts on test

  7. 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 Ft=mDv). 

  8. Impact time—long vs. short • The shorter the impact time the larger the force (WHY???) needed to say “Use the equation J=F*t 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 won’t 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.)

  9. 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 weren’t 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, didn’t talk about any specific examples in Concept Problems 9-12 (bullets, cars, etc)

  10. Impulse Momentum Problems • When finding the change in momentum we use this formula: J=Ft=∆p=pf-pi=mvf=m(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!

  11. 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 Rocio’s club in contact with the club? • M=0.058-kg • F=272N • V=62.0 m/s • UseF x t = m x v • (272N)(t)=(0.058kg)((62.0m/s) • t=0.013 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=?

  12. 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 ball’s change in momentum? What is the bowling ball’s 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 kg*m/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.)

  13. Newton’s 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!

  14. Conserved vs Constant • Excellent defn. BUT, “forces” do not “transfer”. MOMENTUM TRANSFERS. • Better to say: there is no change in any object’s 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. • 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)

  15. The Recoil Effect • Recoil effect can be explained in two different ways: • (A) equal but opposite forces • or (B) the conservation or momentum.... • pit=0 • then if pFa=20 kgm/s, pFb= 20 kgm/s • therefore pFt=0 • And finally, pit=pFt • Didn’t give any specific examples from Concept Problems 22-25 (or lab or cat or hose, etc) and didn’t explain with method A well enough. They would get full credit for method B. 8 points on unit test!!!!!!

  16. 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? • Pit=PFt • (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 J=Ft problems; “bounces”, “head-on”, “hit back” are all words to mean one of the velocities will be negative!

  17. Take this self-QUIZ: • Write EACH of Newton’s 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 N’s 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??

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