Momentum and Its Relation to Force
|
|
- Rosamond Alexander
- 5 years ago
- Views:
Transcription
1 Linear Momentum
2 Momentum and Its Relation to Force Momentum is a vector symbolized by the symbol p, and is defined as: It is a vector and has units of: (kg m/s) or (Ns) The rate of change of momentum is equal to the average net force: This can be shown using Newton s second law. F Net = ma = m Δ v Δt = m v f v i Δt = m v f m " v i Δt F Net = Δ p Δt F Net Δt = m v f m " v i = p f p i = Δ p F Net Δt = Δ p or F Net = Δ p Δt
3 Example 1: If a 1200 kg car has a momentum of 1.50x10 4 kg/s North, what is its velocity? Answer:12.5 m/s North Solution: p=mυ υ = p/m = (1.50x10 4 )/1200 = 12.5 m/s North The momentum vector has the same direction as the velocity vector.
4 Impluse is defined as an object s change in momentum (Δp). Impulse must also be a vector. On slide#2 it was shown how an object s change in momentum was related to force: F Net Δt = Δ p where Δ p = p f p i Example 2: (1-d vector problem) An 5.00 kg object was travelling to the right with a speed of 3.00 m/s. In a time of 1.20 s it slowed to speed of 1.00 m/s travelling in the same direction. a) What was the object s change in momentum? b) What average net force acted on the object?
5 Solution example 2: a) Sketch a diagram first, and define a positive direction : +X 3 m/s 1.00 m/s Δ p = p f p i Before After = (5)(1) - (5)(3)= -10 kg m/s b) F Net = Δ p Δt = -10/1.2= N
6 Example 3: A 5.00 kg object travelling to the right at 6.00 m/s collided with a wall and bounced back at 4.00 m/s in the opposite direction. a) What was the object s impulse? b) If the wall exerted an average force of 120 N on the object in the collision, for how long was the object in contact with the wall?
7 Example 3 Solution(1-d vector problem) : a) Before After 6.00 m/s 4.00 m/s +X Δ p = p f p i b) Δt = Δ p F Net = (5)(-4) (5)(6) = Ns = (-50)/(-120) = 0.42 s Recall that momentum units can be stated Ns or Kg m/s. They are both part of the mks system.
8 Examining momentum in 2- dimensions does not pose any difficulties to someone who understands 2-d vector analysis. The principles (definitions) of momentum in 1-d and 2-d are the same. Example 4 (2d vector problem) : A 5.00 Kg mass had an initial velocity of 3.00 m/s north. In a time of 2.43 s its velocity changed to 4.00 m/s East. a) What was the impulse of the mass? b) What average force acted on the mass over its momentum change?
9 Solution Example 4: a) p i = (5)(3) = 15 Ns north Before 3 m/s After p f = (5)(4) = 20 Ns East 4 m/s Δ p = p f p Use components or head to i tail method to solve for vector Δp Δ p = p f + ( p i ) p f = 20 Ns Δp = (15) 2 + (20) 2 = 25.0 Ns - p i = 15 Ns Θ= tan -1 ( 15/20)= S of E Δp =? b) F Net = Δ p Δt = 25/2.43 = 10.3 N S of E
10 Example 5 (2d vector problem) : An airplane (m= 3.50x10 5 kg) had an initial velocity of 400 km/h north. A net force of 2.48x10 5 N 71 0 E of S, acted on the plane for a time of 3.00 minutes. What was the final velocity (in km/h) of the plane? Find Impulse 1 st. One could solve using adding vectors head to tail but in this case solve using vector components for practice.
11 Solution Example 5: Δ p = p f p i p f = Δ p + p i Pi = 400 Km/h = 3.889x10 7 Ns North ΔP =FΔt (2.48x10 5 )[(3)(60)] = 4.464x10 7 Ns 71 0 E of S Using components: p fx = Δ p x + p ix = (4.464x10 7 )cos(19 0 ) + 0 = x10 7 Ns p fy = Δ p y + p iy = ( x10 7 )sin(19 0 ) x10 7 = x10 7 Ns p f = p 2 fx + p 2 fy = ( x 10 7 ) 2 + ( x 10 7 ) 2 = x10 7 Ns N of E p f p fx p fy Θ = tan -1 (pfy/pfx) = υ = p m = (4.873 x107 )/(3.50x10 5 )= 139 m/s = 501 km/h N of E Retry this problem by adding vectors head to tail and solving for P f using cosine and sine laws.
12 Collisions and Impulse During a collision, objects are deformed due to the large forces involved. In a collision there is an average net force that acts on the object. There is also an equal and opposite force acting on the other surface (Newton s 3 rd Law).
13 The graphs below show a typical collision (usually some sort of bell curve). The force of contact (reaction force) versus the time of contact. The area under the curve equals the impulse (recall Δp=FΔt), where F is the average net force.
14 Example 6: A kg mass approached a wall with a speed of 2.00 m/s. If the graph (triangle) below shows the magnitude of force that the mass experienced while in contact with the wall, determine the speed it left the wall with. Depending on the definition of + direction the impluse (area) could be defined by a + or - value. Be careful. Sketch a diagram and define direction. F(N) (50 ms, 35 N) 30 Area of triangle =0.5 (base)(height) F Net Δt = Δ p = " p f p i t (ms)
15 Example 6 solution: It is an arbitrary decision to define a + direction. Let the + direction be to the right (same direction as initial velocity). F Net Δt = Δ p = " p f p i Before x+ 2 m/s After F W A L L One can use the area under the curve to obtain the magnitude of the impulse. Area = (0.5)( 100 x10-3 s)(35 N) = 1.75 Ns One can see that the direction of the impulse (same direction as average net force on object) is to the left, so it should take on a - value. F Net Δt = Δ p = " p f p i = (0.5)υ (0.5)(2) υ= m/s speed = 1.50 m/s
16 The impulse tells us that we can get the same change in momentum with a large force acting for a short time, or a small force acting for a longer time. This is why you should bend your knees when you land; why airbags work; and why landing on a pillow hurts less than landing on concrete. There are of course less severe examples to test these concepts.
17 The Law of Conservation of Momentum During a collision, measurements show that the total momentum does not change. The total momentum before collision equals the total momentum after collision. p Total Before = p Total After F F During the collision there are equal and opposite forces. This means the impulse of each of the objects are equal in magnitude but in opposite directions. The sum of both impulses is equal to zero meaning there is no net change in the total momentum of the system (system = both masses). This indicates that the total momentum of the system should remain constant. Momentum conservation follows from Newton s 3 rd law.
18 The total momentum of an isolated system of objects remains constant. The total momentum of the system before collision (explosion) is equal to the total momentum after collision. It should be noted that even in an explosion, where potential energy is changed to kinetic, newton s 3 rd law applies.
19 Momentum conservation works for a rocket as long as we consider the rocket and its fuel to be one system, and account for the mass loss of the rocket.
20 Momentum is conserved in all collisions (explosions). Collisions in which kinetic energy is conserved as well are called elastic collisions, and those in which it is not are called inelastic. Often to emphasize that a collision is elastic, one calls it a perfectly elastic collision. If the two objects stick together after collision it is called a completely inelastic collision.
21 Most collisions are inelastic. With inelastic collisions, some of the initial kinetic energy is lost to other forms of energy such as thermal or sound energy. See the example on the next slide.
22 Cars and Cliffs
23 1-D conservation of Momentum Examples When solving any momentum problem get into the habit of drawing a diagram of before and after. Define your directions. State the relevant law or relationship. Obtain equation(s) and solve. Example 7: A 4.00 kg object was travelling east at 2.00 m/s and collided with a 3.00 kg object travelling west at 1.00 m/s. After the collision the 3.00 kg object had a speed of 1.00 m/s in the opposite direction (east) a) What was the velocity of the 4.00 kg mass after the collision? b) Was this a perfectly elastic collision? Compare the total kinetic energy (of both objects) before and after the collision. c) What kind of collision was it?
24 Example 7 solution: First sketch a diagram and define a positive direction. x+ 2 m/s 1 m/s 1 m/s 4 kg 3 kg 4 kg 3 kg a) p Total Before = p Total After Before (4)(2) + (3)(-1) = 4υ + (3)(1) υ= 0.50 m/s After b) E K total before = (0.5)(4)(2) 2 + (0.5)(3)(1) 2 = 9.50 J E K total after = (0.5)(4)(0.5) 2 + (0.5)(3)(1) 2 = 2.00 J There was 7.50 J lost it is not a perfectly elastic collision c) It was an inelastic collision since some kinetic energy changed form. Note that the kinetic energy ( always be a positive number. 1 2 mυ 2 )of any object must
25 Example 8: A 10.0 kg object was initially travelling West (to the left) at 15 m/s and exploded into two pieces. A 4.00 kg piece after the explosion was travelled 7.50 m/s East (to the right). a) What was the velocity of the other piece after the explosion? b) How could one verify that this was indeed an explosion and not a typical collision?
26 Solution Example 8: Draw a diagram and define a direction. I labeled the unknown velocity υ in the direction of +x. One would expect that υ must be in the other direction, so a negative value is expected. x+ a) p Total Before = p Total After 15 m/s 10.0 kg 4 kg Before 7.50 m/s (10)(-15) = (6)υ + (4)(7.5) υ= -30 m/s, or 30 m/s left. One must clearly indicate a direction when stating momentum (unless stated otherwise). =? After b) One can determine that it must be an explosion by calculating the total kinetic energy after and before the explosion. If the total kinetic energy is greater after the explosion than before some form of potential energy must have been converted into kinetic energy (i.e in an explosion).
27 Example 9: A 4.00 kg mass travelling at 5.00 m/s to the right had a completely inelastic collision with a 7.00 kg mass travelling at 4.00 m/s in the opposite direction. What was the velocity of the masses after the collision?
28 Example 9 solution: If it is completely inelastic then the two objects join or stick together. One can treat it the masses after collision as a combined mass. p Total Before = p Total After 5 m/s 4 m/s 4 kg 7 kg Before x+ 11 kg After (4)(5) + (7)(-4) = 11υ υ = m/s or 0.73 m/s left
29 Here we have two objects colliding elastically. We know the masses and the initial speeds. Since both momentum and kinetic energy are conserved, we can write two equations. This allows us to solve for the two unknown final speeds.
30 Example 10: A 2.00 kg object was travelling at 4.00 m/s to the right and collided perfectly elastically with a 3.00 kg object travelling to the left at 1.50 m/s. Set up the two equations necessary to solve for the unknown velocities after the collision. Always draw a before and after collision diagram.
31 Example 10 solution: x+ Before Collision After Collision 2 kg 3 kg kg 3 kg 4 m/s 1.5 m/s Momentum is conserved: p Total Before = p Total After (2)(4)+(3)(-1.5) = 2υ 1 + 3υ 2 Kinetic energy is conserved: 3.5 = 2υ 1 + 3υ 2 Total kinetic energy before collision = Total kinetic energy after collision (0.5)(2)(4) 2 + (0.5)(3)(1.5) = (0.5)(2) υ 1 + (0.5)(3) υ = υ υ 2 2 For a challenge solve the system of equations to find the unknown velocities after the collision.
32 Additional Momentum/Energy Problems: Example 11(harder): Two stationary masses (one mass is double the mass of the other) on a frictionless have a compressed spring sandwiched between them. The spring is released and the smaller mass (m) had a velocity υ after the release of the spring. What was the amount of stored energy (in terms of m and υ) in the spring if 80 % of this energy went into the movement of the masses? Use momentum 1 st. m Before compressed spring 2m frictionless ground m m After frictionless ground 2m '=?
33 Example 11 solution: p Total Before = p Total After + 0 = -mυ + 2mυ υ = 0.5υ The total kinetic energy of the objects after the spring released its energy is : 0.5mυ (2m)(0.5υ) 2 = (0.75)mυ 2 Only 80% of the store energy went into the movement of the objects, therefore the energy E initially stored in the spring is: (0.80)E =(0.75) mυ 2 E= (0.938)mυ 2
34 Example 12: A gram bullet travelling horizontally at 285 m/s struck a stationary 1.35 Kg pendulum and had a speed of 80.0 m/s after it passed through the pendulum mass. To what vertical height did the pendulum swing to? Start with momentum (collision) then use energy conservation. Before After h=? 285 m/s 80 m/s
35 Example 12 solution: ptotal Before = p Total After + (0.015)(285) = (0.015)(80) + (1.35)υ υ = m/s Conservation of mechanical energy: 1 2 mυ 2 = mgh 1 2 υ 2 = gh h = (2.778) 2 / [2(9.80)] = m
36 Conservation of energy and momentum can also be used to analyze collisions in two or three dimensions, but unless the situation is very simple, the math quickly becomes unwieldy. Here, a moving object collides with an object initially at rest. Knowing the masses and initial velocities is not enough; we need to know the angles as well in order to find the final velocities.
37 Example 13 (2-d): A 2.00 kg object was initially travelling east at 10.0 m/s and collided with a stationary 8.00 kg mass. After the collision the 2.00 kg mass had velocity of 5.00 m/s 30 0 N of E. What was the velocity of the 8.00 Kg mass after the collision? Steps to follow: 1) Sketch a diagram (before and after collision). 2) Define your momentum vectors 3) State a vector relationship dictated by conservation of momentum. 4) Draw the vector diagram according to how the three momentum vectors are related. 5) Use cosine and sine laws to find the unknown momentum vector.6) Determine velocity. One could also use components to do this problem. Make sure that you can apply components to this problem.
38 Example 13 solution: p 1 = 20 Ns East p 2 p 3 =? = 10 Ns 30 0 N of E Conservation of momentum: Vector relationship: W N S 2 kg E Before 10 m/s p 1 p Total Before = p Total After p 1 = p 2 + p 3 v= 0 8 kg After p 2 5 m/s 2 kg kg p 3? Vector diagram: p 2 = 10 Ns p 3 = (10)(20)cos30 0 = Ns p 3 =? 30 0 p 1 = 20 Ns υ = p m = /8 = 1.55 m/s sinθ 10 = sin In summary, Θ= υ = 1.55 m/s S of E
39 Often the choice to use components or not, is just an arbitrary decision. There are some circumstances however where components may be more convenient. The case where there are more than 3 momentum vectors involved makes the choice much easier. In the following example, using components is the way to go. Example 14 (2-d): A 10.0 kg object with some unknown velocity exploded into 3 pieces. After the explosion the 2.00 kg piece travelled north at 4.00 m/s, the 5.00 kg piece travelled East at 6.00 m/s, and the remaining piece travelled at 8.00 m/s 30 0 E of S. What was the velocity of the 10.0 kg piece before the collision? Steps to follow: 1) Sketch a diagram (before and after collision). 2) Define your momentum vectors 3) State a vector relationship dictated by conservation of momentum. 4) Determine the x and y components of all vectors. 6) Using the vector relationship solve for the unknown x and y components. 7) Determine the magnitude and direction of the unknown momentum vector.
40 Example 14 Solution: p 1 =? p 2 = 8 Ns N p 3 = 30 Ns E P 4 = 24 Ns 30 0 E of S p 2x = 0, p 2y = 8 Ns p 3x = 30 Ns, p 3y = 0 P 4x = 24(cos60) Ns p 4y = -(24)(sin60) Ns Before 10 kg p Total Before = p p1 Total After = p 2 + p 3 + p 4 p 1x = p 2 x + p 3x + p 4 x +y +x p 1 =? = (cos60) = 42 Ns After p 2 4 m/s 2 kg 5 kg kg 8 m/s p 4 6 m/s p 3 p 1y = p 2 y + p 3y + p 4 y = (sin60) = Ns 42 Ns p Ns p 1 = p 2 1x + p 1y " θ = tan % $ # 42 & 2 = Ns υ = p 1 m = 43.9/10= 4.39 m/s ' = υ = 4.39 m/s S of E
Conservation of Momentum
Conservation of Momentum Newton: Quantity of Motion Forces applied for a period of time change an object s quantity of motion. F = ma F = m Δ v t F t = mδv = mv f mv i p mv Ft = Δp F = dp dt Conservation?
More informationCh 7 Impulse-Momentum Theorem, Conservation of Momentum, and Collisions
Ch 7 Impulse-Momentum Theorem, Conservation of Momentum, and Collisions Momentum and its relation to force Momentum describes an object s motion. Linear momentum is the product of an object s mass and
More informationSlide 1 / 47. Momentum by Goodman & Zavorotniy
Slide 1 / 47 Momentum 2009 by Goodman & Zavorotniy Slide 2 / 47 Conservation of Momentum s we pointed out with energy, the most powerful concepts in science are called "conservation principles". These
More informationLecture PowerPoints. Chapter 7 Physics: Principles with Applications, 7 th edition Giancoli
Lecture PowerPoints Chapter 7 Physics: Principles with Applications, 7 th edition Giancoli This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching
More informationImpulse simply refers to a change in momentum, and is usually caused by a change in velocity, as described by p = m v.
1 Impulse and Momentum Recall from Newton s 1 st Law: inertia is the tendency of an object to keep on doing what its already doing, that is: either remaining stationary, or: travelling at a constant velocity.
More informationImpulse (J) J = FΔ t Momentum Δp = mδv Impulse and Momentum j = (F)( p = ( )(v) F)(Δ ) = ( )(Δv)
Impulse (J) We create an unbalancing force to overcome the inertia of the object. the integral of force over time The unbalancing force is made up of the force we need to unbalance the object and the time
More informationMomentum. Slide 1 / 47. Slide 2 / 47. Slide 3 / 47. Conservation of Momentum. Conservation of Momentum
Slide 1 / 47 Momentum 2009 by Goodman & Zavorotniy onservation of Momentum Slide 2 / 47 s we pointed out with energy, the most powerful concepts in science are called "conservation principles". These principles
More informationConservation of Momentum
Conservation of Momentum Law of Conservation of Momentum The sum of the momenta before a collision equal the sum of the momenta after the collision in an isolated system (=no external forces acting).
More informationMomentum Conceptual Questions. 1. Which variable has more impact on an object s motion? Its mass or its velocity?
AP Physics I Momentum Conceptual Questions 1. Which variable has more impact on an object s motion? Its mass or its velocity? 2. Is momentum a vector or a scalar? Explain. 3. How does changing the duration
More informationMomentum. Slide 2 / 69. Slide 1 / 69. Slide 4 / 69. Slide 3 / 69. Slide 5 / 69. Slide 6 / 69. Conservation of Momentum. Conservation of Momentum
Slide 1 / 69 Momentum 2009 by Goodman & Zavorotniy Slide 2 / 69 onservation of Momentum The most powerful concepts in science are called "conservation principles". Without worrying about the details of
More informationOctober 24. Linear Momentum: - It is a vector which may require breaking it into components
October 24 Linear Momentum: - It is a vector which may require breaking it into components Newton s First Law: A body continues with Constant Linear Momentum unless it is acted upon by a Net External Force.
More informationCenter of Mass & Linear Momentum
PHYS 101 Previous Exam Problems CHAPTER 9 Center of Mass & Linear Momentum Center of mass Momentum of a particle Momentum of a system Impulse Conservation of momentum Elastic collisions Inelastic collisions
More informationPhysics 111: Mechanics Lecture 8
Physics 111: Mechanics Lecture 8 Bin Chen NJIT Physics Department Chapter 8 Momentum, Impulse, and Collisions q q q q q q 8.1 Momentum and Impulse 8.2 Conservation of Momentum 8.3 Momentum Conservation
More informationMomentum Practice Problems
Momentum Practice Problems PSI AP Physics C Name Multiple Choice 1. A steel ball and a piece of clay have equal mass. They are dropped from the same height on a horizontal steel platform. The ball bounces
More information1 kg. 10,000 kg. 1 Page. Momentum is a vector so it has a magnitude and a velocity. Its magnitude is the product of its mass and velocity, p = mv.
Momentum The momentum of a single object is simply equal to the product of its mass and its velocity. The symbol for momentum is p. Since mass is a scalar and velocity is a vector, momentum is also a vector.
More informationChapter 9. Linear Momentum and Collisions
Chapter 9 Linear Momentum and Collisions Momentum Analysis Models Force and acceleration are related by Newton s second law. When force and acceleration vary by time, the situation can be very complicated.
More informationGeneral Physics I Momentum
General Physics I Momentum Linear Momentum: Definition: For a single particle, the momentum p is defined as: p = mv (p is a vector since v is a vector). So p x = mv x etc. Units of linear momentum are
More informationChapter 9 Linear Momentum
Chapter 9 Linear Momentum 7 12/7 16/7 Units of Chapter 9 Momentum, Impulse and Collisions Momentum and Impulse Define momentum Force and rate of change of momentum; resultant force as rate of change of
More informationChapter 7 Linear Momentum
Chapter 7 Linear Momentum Units of Chapter 7 Momentum and Its Relation to Force Conservation of Momentum Collisions and Impulse Conservation of Energy and Momentum in Collisions Elastic Collisions in One
More informationPhysics 110 Homework Solutions Week #6 - Wednesday
Physics 110 Homework Solutions Week #6 - Wednesday Friday, May3, 2013 Chapter 6 Questions - none Multiple-Choice 66 C 67 D 68 B 69 C Problems 612 It s velocity as the ball hits the ground is found from
More informationPhysics 2514 Lecture 26
Physics 2514 Lecture 26 P. Gutierrez Department of Physics & Astronomy University of Oklahoma Physics 2514 p. 1/12 Review We have defined the following using Newton s second law of motion ( F net = d p
More informationA. Incorrect! Remember that momentum depends on both mass and velocity. B. Incorrect! Remember that momentum depends on both mass and velocity.
AP Physics - Problem Drill 08: Momentum and Collisions No. 1 of 10 1. A car and motor bike are travelling down the road? Which of these is a correct statement? (A) The car will have a higher momentum.
More informationMechanics. Time (s) Distance (m) Velocity (m/s) Acceleration (m/s 2 ) = + displacement/time.
Mechanics Symbols: Equations: Kinematics The Study of Motion s = distance or displacement v = final speed or velocity u = initial speed or velocity a = average acceleration s u+ v v v u v= also v= a =
More informationMomentum & Energy Review Checklist
Momentum & Energy Review Checklist Impulse and Momentum 3.1.1 Use equations to calculate impulse; momentum; initial speed; final speed; force; or time. An object with a mass of 5 kilograms is moving at
More informationMomentum and Impulse Practice Multiple Choice
Choose the alternative that best answers the question and record your answer on the Scantron sheet provided 1. A ball of putty is thrown at a wall and sticks to its surface. Which of the following quantities
More informationPer 3 4 Momentum_Presentation.notebook. January 23, Momentum.
Momentum www.njctl.org 1 Momentum Click on the topic to go to that section Momentum Impulse Momentum of a System of Objects Conservation of Momentum Inelastic Collisions and Explosions Elastic Collisions
More informationPer 9 10 Momentum_Presentation.notebook. January 20, Momentum.
Momentum www.njctl.org 1 Momentum Click on the topic to go to that section Momentum Impulse Momentum of a System of Objects Conservation of Momentum Inelastic Collisions and Explosions Elastic Collisions
More informationAP Physics Momentum Practice Test. Answers: A,E,E,A,E,B,D,C,B,A,B,E,D,C 16.(a)5450,5650 (b)2.25e7 (c)3 (d)1.5e7 17.(a)9 (b)2 (c)1.5 (d) (e).
AP Physics Momentum Practice Test Answers: A,E,E,A,E,B,D,C,B,A,B,E,D,C 16.(a)5450,5650 (b).5e7 (c)3 (d)1.5e7 17.(a)9 (b) (c)1.5 (d)-4.75 (e).65 For multiple choice ( points) write the CAPITAL letter of
More information23. A force in the negative direction of an x-axis is applied for 27ms to a 0.40kg ball initially moving at 14m/s in the positive direction of the
23. A force in the negative direction of an x-axis is applied for 27ms to a 0.40kg ball initially moving at 14m/s in the positive direction of the axis. The force varies in magnitude, and the impulse has
More informationCHAPTER 9 LINEAR MOMENTUM AND COLLISION
CHAPTER 9 LINEAR MOMENTUM AND COLLISION Couse Outline : Linear momentum and its conservation Impulse and Momentum Collisions in one dimension Collisions in two dimension The center of mass (CM) 9.1 Linear
More informationThink-Pair-Share. Linear Momentum (Ch 9) Linear Momentum, cont. Newton and Momentum
Linear Momentum (Ch 9) The linear momentum of a particle or an object that can be modeled as a particle of mass m moving with a velocity v is defined to be the product of the mass and velocity: p = m v
More informationName ID Section. 1. One mile is equal to 1609 m; 1 hour is equal to 3600 s. The highway speed limit of 65 mph is equivalent to the speed of:
The exam is closed book and closed notes. There are 30 multiple choice questions. Make sure you put your name, section, and ID number on the SCANTRON form. The answers for the multiple choice Questions
More informationThis Week. 9/5/2018 Physics 214 Fall
This Week Momentum Is momentum in basketball physics? Rockets and guns How do spaceships work? Collisions of objects They get impulses! Practical Propulsion 9/5/2018 Physics 214 Fall 2018 1 Momentum What
More informationNov. 27, 2017 Momentum & Kinetic Energy in Collisions elastic collision inelastic collision. completely inelastic collision
Nov. 27, 2017 Momentum & Kinetic Energy in Collisions In our initial discussion of collisions, we looked at one object at a time, however we'll now look at the system of objects, with the assumption that
More informationChapter 7- Linear Momentum
Chapter 7- Linear Momentum Old assignments and midterm exams (solutions have been posted on the web) can be picked up in my office (LB-212) All marks, including assignments, have been posted on the web.
More informationHW assignments for Chapter 6 Q 4,5,7,9 P 3,4,6,8,9,10. Chapter 6. Conservation of Linear Momentum and Collisions. Dr.
HW assignments for Chapter 6 Q 4,5,7,9 P 3,4,6,8,9,10 Chapter 6 Conservation of Linear Momentum and Collisions Dr. Armen Kocharian Momentum and Newton s Laws The linear momentum of an object of mass m
More informationThis Week. 7/29/2010 Physics 214 Fall
This Week Momentum Is momentum in basketball physics? Rockets and guns How do spaceships work? Collisions of objects They get impulses! Practical Propulsion 7/29/2010 Physics 214 Fall 2010 1 Momentum What
More informationMomentum: Exercises. 1. An Olympic diver dives off the high-diving platform. The magnitude of his momentum will be a maximum at point
Momentum: Exercises. An Olympic diver dives off the high-diving platform. The magnitude of his momentum will be a maximum at point (a) A. (b) B. (c) C. (d) D. (e) none of the above. 2. An object with mass
More informationConservation of Momentum. Chapter 9: Collisions, CM, RP. Conservation of Momentum. Conservation of Momentum. Conservation of Momentum
P H Y S I C S Chapter 9: Collisions, CM, RP Since impulse = change in momentum, If no impulse is exerted on an object, the momentum of the object will not change. If no external forces act on a system,
More informationAP Physics C: Mechanics Practice (Systems of Particles and Linear Momentum)
AP Physics C: Mechanics Practice (Systems of Particles and Linear Momentum) 1980M2. A block of mass m slides at velocity v o across a horizontal frictionless surface toward a large curved movable ramp
More informationPHYSICS. Chapter 11 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 11 Lecture RANDALL D. KNIGHT Chapter 11 Impulse and Momentum IN THIS CHAPTER, you will learn to use the concepts of impulse and momentum.
More informationMomentum & Energy Review Checklist
Momentum & Energy Review Checklist Impulse and Momentum 3.1.1 Use equations to calculate impulse; momentum; initial speed; final speed; force; or time. An object with a mass of 5 kilograms is moving at
More information6.1 Momentum and Impulse A. What is momentum? Newton defined momentum as the quantity of motion
AP Physics Mechanics Chapter 6 Momentum and Collisions Text chapter 6 - Reading pp. 141-161 - textbook HW -- #1,3,4,6,9,15,16,20,21,23,26,27,25,34,63,70,71 1 6.1 Momentum and Impulse A. What is momentum?
More informationPhysics 10 Lecture 6A. "And in knowing that you know nothing, that makes you the smartest of all. --Socrates
Physics 10 Lecture 6A "And in knowing that you know nothing, that makes you the smartest of all. --Socrates Momentum Which is harder to stop a small ball moving at 1 m/s or a car moving at 1 m/s? Obviously
More informationMomentum and Its Relation to Force
Linear Momentum Momentum and Its Relation to Force The linear momentum, or momentum, of an object is defined as the product of its mass and its velocity. Momentum, p, is a vector and its direction is the
More informationEnergy& Momentum ~Learning Guide Name:
Energy& Momentum ~Learning Guide Name: Instructions: Using a pencil, answer the following questions. The Pre-Reading is marked, based on effort, completeness, and neatness (not accuracy). The rest of the
More informationChapter 9 Linear Momentum and Collisions
Chapter 9 Linear Momentum and Collisions The Center of Mass The center of mass of a system of particles is the point that moves as though (1) all of the system s mass were concentrated there and (2) all
More informationFinal Review. If a car has 3,000kg-m/s of momentum, and a mass of 1,000kg. How fast is it moving? A ball that has momentum must also have energy.
Physics Name: Date: Period: Final Review Write the appropriate formulas with all units below. Impulse Momentum Conservation of Momentum Rank these in order from least to most momentum:.01kg mass moving
More informationHATZIC SECONDARY SCHOOL PROVINCIAL EXAMINATION ASSIGNMENT ENERGY & MOMENTUM MULTIPLE CHOICE / 30 OPEN ENDED / 79 TOTAL / 109 NAME:
HATZIC SECONDARY SCHOOL PROVINCIAL EXAMINATION ASSIGNMENT ENERGY & MOMENTUM MULTIPLE CHOICE / 30 OPEN ENDED / 79 TOTAL / 109 NAME: 1. Which of the following best represents the momentum of a small car
More informationSection 1 Momentum and Impulse. Chapter 6. Preview. Objectives Linear Momentum. Houghton Mifflin Harcourt Publishing Company
Section 1 Momentum and Impulse Preview Objectives Linear Momentum Section 1 Momentum and Impulse Objectives Compare the momentum of different moving objects. Compare the momentum of the same object moving
More informationChapter 9 Impulse and Momentum
Chapter 9 Impulse and Momentum Chapter Goal: To understand and apply the new concepts of impulse and momentum. Slide 9-2 Chapter 9 Preview Slide 9-3 Chapter 9 Preview Slide 9-4 Chapter 9 Preview Slide
More informationAn astronaut of mass 80 kg pushes away from a space Both!p x
Chapter 6 Momentum Collisions Definition: Momentum Important because it is CONSERVED proof: p = m v F = m v t = p t Ft = p Since F 12 =-F 21, p 1 + p 2 = 0 p i for isolated particles never changes Vector
More informationThe SI units of mass are kilograms (kg) and of velocity are meters / second (m/s). Therefore, the units of momentum are kg m/s.
Momentum Introduction As was pointed out in the previous chapter, some of the most powerful tools in physics are based on conservation principles. The idea behind a conservation principle is that there
More informationAP Physics 1 Momentum
Slide 1 / 133 Slide 2 / 133 AP Physics 1 Momentum 2015-12-02 www.njctl.org Slide 3 / 133 Table of Contents Click on the topic to go to that section Momentum Impulse-Momentum Equation The Momentum of a
More informationMomentum and Collisions
Momentum and Collisions Vocabulary linear momemtum second law of motion isolated system elastic collision inelastic collision completly inelastic center of mass center of gravity 9-1 Momentum and Its Relation
More informationCompare the momentum of the same object moving with different velocities. Identify examples of change in the momentum of an object.
HOLT CH 6 notes Objectives :Compare the momentum of different moving objects. Compare the momentum of the same object moving with different velocities. Identify examples of change in the momentum of an
More information7-6 Inelastic Collisions
7-6 Inelastic Collisions With inelastic collisions, some of the initial kinetic energy is lost to thermal or potential energy. It may also be gained during explosions, as there is the addition of chemical
More information(k = force constant of the spring)
Lecture 10: Potential Energy, Momentum and Collisions 1 Chapter 7: Conservation of Mechanical Energy in Spring Problems The principle of conservation of Mechanical Energy can also be applied to systems
More informationChapter 6 - Linear Momemtum and Collisions
Name Date Chapter 6 - Linear Momemtum and Collisions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) What is the SI unit of momentum? A) N/s B)
More informationAP Physics C Mechanics
1 AP Physics C Mechanics Momentum 2015 12 04 www.njctl.org 2 Table of Contents Conservation of Linear Momentum Impulse Momentum Equation Collisions in One Dimension Collisions in Two Dimensions Center
More informationImpulse and Momentum continued
Chapter 7 Impulse and Momentum continued 7.2 The Principle of Conservation of Linear Momentum External forces Forces exerted on the objects by agents external to the system. Net force changes the velocity
More informationSometimes (like on AP test) you will see the equation like this:
Work, Energy & Momentum Notes Chapter 5 & 6 The two types of energy we will be working with in this unit are: (K in book KE): Energy associated with of an object. (U in book PE): Energy associated with
More informationChapter 7. Impulse and Momentum
Chapter 7 Impulse and Momentum 1) Linear momentum p = mv (units: kg m / s) 2) Impulse (produces a finite change in momentum) (a) Constant force: J = FΔt From the 2nd law, F = Δ(m v) Δt = Δ p Δt, so J =
More informationImpulse/Momentum And Its Conservation
Impulse/Momentum And Its Conservation Which is easier to stop? Truck, car, bowling ball, or baseball all moving at 30 mph. Baseball -it is the least massive. Baseball at 30 mph or a baseball at 90 mph.
More informationfrictionless horizontal surface. The bullet penetrates the block and emerges with a velocity of o
AP Physics Free Response Practice Momentum and Impulse 1976B2. A bullet of mass m and velocity v o is fired toward a block of mass 4m. The block is initially at rest on a v frictionless horizontal surface.
More informationMomentum and Collisions
Momentum and Collisions Objectives: You Should Be Able To: Define and give examples of impulse and momentum along with appropriate units. Write and apply a relationship between impulse and momentum in
More informationMomentum in 1-Dimension
Momentum in 1-Dimension Level : Physics I Date : Warm-up Questions If you were in a car that was out of control and had to choose between hitting a concrete wall or a haystack to stop, which would you
More information1. A 1,160-kg car traveling initially with a speed of 25.0 m/s in an easterly direction crashes into the rear end of a
Collisions Worksheet Honors: Name: Date: 1. A 1,160-kg car traveling initially with a speed of 25.0 m/s in an easterly direction crashes into the rear end of a 9,900-kg truck moving in the same direction
More informationConservation of Momentum. Last modified: 08/05/2018
Conservation of Momentum Last modified: 08/05/2018 Links Momentum & Impulse Momentum Impulse Conservation of Momentum Example 1: 2 Blocks Initial Momentum is Not Enough Example 2: Blocks Sticking Together
More informationMomentum. Slide 1 / 140. Slide 2 / 140. Slide 3 / 140. Table of Contents.
Slide 1 / 140 Slide 2 / 140 Momentum www.njctl.org Table of Contents Slide 3 / 140 Click on the topic to go to that section Conservation of Linear Momentum Impulse - Momentum Equation Collisions in One
More information1 A freight car of mass 20,000 kg moves along a frictionless level railroad track with a constant speed of 15 m/s. What is the momentum of the car?
Slide 1 / 26 1 freight car of mass 20,000 kg moves along a frictionless level railroad track with a constant speed of 15 m/s. What is the momentum of the car? 30,000 kg m/s 3,000 kg m/s 300,000 kg m/s
More informationPhysics 131: Lecture 15. Today s Agenda
Physics 131: Lecture 15 Today s Agenda Impulse and Momentum (or the chapter where physicists run out of letters) Non-constant t forces Impulse-momentum thm Conservation of Linear momentum External/Internal
More informationp p I p p p I p I p p
Net momentum conservation for collision on frictionless horizontal surface v1i v2i Before collision m1 F on m1 from m2 During collision for t v1f m2 F on m2 from m1 v2f +x direction After collision F F
More informationDO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN. Physics FINAL EXAMINATION June 2011.
Name: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN Value: 80 Marks Physics 2204 FINAL EXAMINATION June 2011 General Instructions This examination consists of
More information6 th week Lectures Feb. 12. Feb
Momentum Rockets and guns 6 th week Lectures Feb. 12. Feb. 16. 2018. How do spaceships work? Collisions of objects They get impulses! Practical Propulsion 2/11/2018 Physics 214 Spring 2018 1 Announcements
More informationChapter Work, Energy and Power. Q1. The co-efficient of restitution e for a perfectly elastic collision is [1988] (a) 1 (b) 0 (c) (d) 1 Ans: (a)
Chapter Work, Energy and Power Q1. The co-efficient of restitution e for a perfectly elastic collision is [1988] (a) 1 (b) 0 (c) (d) 1 Q2. A bullet of mass 10g leaves a rifle at an initial velocity of
More informationMomentum. Slide 1 / 140. Slide 2 / 140. Slide 3 / 140. Table of Contents.
Slide 1 / 140 Slide 2 / 140 Momentum www.njctl.org Table of Contents Slide 3 / 140 Click on the topic to go to that section Conservation of Linear Momentum Impulse - Momentum Equation Collisions in One
More informationPHYS 154 Practice Test 3 Spring 2018
The actual test contains 1 multiple choice questions and 2 problems. However, for extra exercise, this practice test includes 4 problems. Questions: N.B. Make sure that you justify your answers explicitly
More information(A) 0 (B) mv (C) 2mv (D) 2mv sin θ (E) 2mv cos θ
Physics 1 Lesson 8 Forces and Momentum Homework Outcomes 1. Define linear momentum. 2. Determine the total linear momentum of a system. 3. Apply the Law of Conservation of Momentum to solve problems. 4.
More informationWallace Hall Academy
Wallace Hall Academy CfE Higher Physics Unit 1 - Dynamics Notes Name 1 Equations of Motion Vectors and Scalars (Revision of National 5) It is possible to split up quantities in physics into two distinct
More informationΣp before ± I = Σp after
Transfer of Momentum The Law of Conservation of Momentum Momentum can be transferred when objects collide. The objects exert equal and opposite forces on each other, causing both objects to change velocity.
More informationMomentum. A ball bounces off the floor as shown. The direction of the impulse on the ball, is... straight up straight down to the right to the left
Momentum A ball bounces off the floor as shown. The direction of the impulse on the ball,, is... A: B: C: D: straight up straight down to the right to the left This is also the direction of Momentum A
More informationConceptual Physics Final Exam Review
Useful Information Work and Energy W = F x W = work [J] F = force [N] x = displacement [m] U g = mgh U g = gravitational potential energy [J] m = mass [kg] h = height [m] g = 10 m/s 2 DC Circuits I =!!
More informationWhat is momentum? Inertia in Motion.
What is momentum? Inertia in Motion. p = mv From Newton s 2 nd Law: F = ma = dv d( mv) m = dt dt F = dp dt The time rate of change of the linear momentum of a particle is equal to the net force acting
More informationMomentum_P2 1 NA 2NA. 3a. [2 marks] A girl on a sledge is moving down a snow slope at a uniform speed.
Momentum_P2 1 NA 2NA 3a. [2 marks] A girl on a sledge is moving down a snow slope at a uniform speed. Draw the free-body diagram for the sledge at the position shown on the snow slope. 3b. [3 marks] 1
More informationExtra credit assignment #4 It can be handed in up until one class before Test 4 (check your course outline). It will NOT be accepted after that.
Extra credit assignment #4 It can be handed in up until one class before Test 4 (check your course outline). It will NOT be accepted after that. NAME: 4. Units of power include which of the following?
More informationAlgebra Based Physics
1 Algebra Based Physics Momentum 2016 01 20 www.njctl.org 2 Momentum Click on the topic to go to that section Momentum Impulse Momentum of a System of Objects Conservation of Momentum Inelastic Collisions
More informationChapter 8 LINEAR MOMENTUM AND COLLISIONS
Chapter 8 LINEAR MOMENTUM AND COLLISIONS Linear Momentum Momentum and Newton s Second Law Impulse Conservation of Linear Momentum Inelastic Collisions Elastic Collisions Center of Mass Systems with Changing
More informationAP Physics 1. Momentum. Slide 1 / 133 Slide 2 / 133. Slide 3 / 133. Slide 4 / 133. Slide 5 / 133. Slide 6 / 133. Momentum.
Slide 1 / 133 Slide 2 / 133 AP Physics 1 Momentum 2015-12-02 www.njctl.org Slide 3 / 133 Slide 4 / 133 Table of Contents Click on the topic to go to that section Momentum Impulse-Momentum Equation The
More informationREVISING MECHANICS (LIVE) 30 JUNE 2015 Exam Questions
REVISING MECHANICS (LIVE) 30 JUNE 2015 Exam Questions Question 1 (Adapted from DBE November 2014, Question 2) Two blocks of masses 20 kg and 5 kg respectively are connected by a light inextensible string,
More informationWelcome back to Physics 211
Welcome back to Physics 211 Today s agenda: Impulse and momentum 09-2 1 Current assignments Reading: Chapter 10 in textbook Prelecture due next Tuesday HW#8 due this Friday at 5 pm. 09-2 2 9-2.1 A crash
More informationIMPACT Today s Objectives: In-Class Activities:
Today s Objectives: Students will be able to: 1. Understand and analyze the mechanics of impact. 2. Analyze the motion of bodies undergoing a collision, in both central and oblique cases of impact. IMPACT
More information(D) Based on Ft = m v, doubling the mass would require twice the time for same momentum change
1. A car of mass m, traveling at speed v, stops in time t when maximum braking force is applied. Assuming the braking force is independent of mass, what time would be required to stop a car of mass m traveling
More informationPhysics 231 Lecture 14
Physics 231 Lecture 14 Impulses: forces that last a short time Momentum: p = mv Impulse-Momentum theorem: FΔt = Δp = mδv = m( v f v i ) Momentum conservation: p tot,f p 1,f + p 2,f = p 1,i + p 2,i p tot,i
More informationObjectives 326 CHAPTER 7 MOMENTUM
Objectives Define linear momentum. Explain the relationship between force and rate of change of momentum. Define impulse. Explain the relationship between impulse and change in momentum. Explain Newton
More informationChapter 9. Linear Momentum
Chapter 9 Linear Momentum Linear Momentum Conservation of Linear Momentum Kinetic Energy of a System Collisions Collisions in Center of Mass Reference Frame MFMcGraw-PHY 45 Chap09Ha-Momentum-Revised-10//01
More informationPhysics 2211 ABC Quiz #4 Solutions Spring 2017
Physics 22 ABC Quiz #4 Solutions Spring 207 I. (6 points) Corentine is driving her car of mass m around a curve when suddenly, all systems fail! The engine quits, she can t brake, she can t steer, and
More informationIMPACT (Section 15.4)
IMPACT (Section 15.4) Today s Objectives: Students will be able to: a) Understand and analyze the mechanics of impact. b) Analyze the motion of bodies undergoing a collision, in both central and oblique
More informationMomentum and impulse Book page 73-79
Momentum and impulse Book page 73-79 Definition The rate of change of linear momentum is directly proportional to the resultant force acting upon it and takes place in the direction of the resultant force
More informationAP Physics C. Momentum. Free Response Problems
AP Physics C Momentum Free Response Problems 1. A bullet of mass m moves at a velocity v 0 and collides with a stationary block of mass M and length L. The bullet emerges from the block with a velocity
More information