Conservation Laws Conservation of Momentum II

Slides:



Advertisements
Similar presentations
Hints and Examples from Chapter 8
Advertisements

Physics 11 Mr. Jean November 28 th, The plan: Video clip of the day 2d Momentum Momentum practice questions Physics Video.
2. (15 points) An incident ball A of mass kg is sliding at 1.4 m/s on the horizontal tabletop of negligible friction shown above. It makes a head-on.
Conservation of Momentum
Center of Mass and Linear Momentum
Momentum and Energy in Collisions. A 2kg car moving at 10m/s strikes a 2kg car at rest. They stick together and move to the right at ___________m/s.
Elastic Collisions. Conservation  Elastic collisions conserve both momentum and kinetic energy.  Two equations govern all elastic collisions. m1m1 m2m2.
Elastic Collisions. Momentum and Kinetic Energy  An object in motion has a momentum based on its mass and velocity. p = mvp = mv  The object also has.
Momentum and Impulse.
1.4 MOMENTUM IN TWO DIMENSIONS. Momentum momentum of an object to be the product of mass (m) and velocity (v). Momentum is a vector quantity with SI Units.
Principles of Physics. - property of an object related to its mass and velocity. - “mass in motion” or “inertia in motion” p = momentum (vector) p = mvm.
AP Physics I.D Impulse and Momentum. 7.1 Impulse-Momentum Theorem.
Ch. 8 Momentum and its conservation
Unit 1 – Momentum and Impulse
Linear Momentum AP Physics C. What is Momentum? What is its definition? Momentum: the product of an object’s mass and its velocity Momentum: “mass in.
Notes: Chapter 11.3 Newton’s Third Law of Motion and Momentum.
Do now! Can you continue the sheet you started yesterday on stopping distances?
Do now! Can you talk with your partner about what we learned last lesson?
Chapter 9: Linear Momentum & Collisions
Momentum An object of mass m traveling at velocity has a linear momentum (or just momentum),, given by Units have no special name: kg-m/s With no net force.
The product of mass and velocity of a body is called momentum. Force and Laws of Motion Momentum Mathematically, Momentum = mass × velocity P = mv It is.
Newton’s Laws of Motion
Momentum Ms. Li Momentum is a commonly used term in sports. A team that has the momentum is on the move and is going to take some effort to stop. A team.
Physics 218 Lecture 15: Momentum Alexei Safonov.
Systems of Particles. Rigid Bodies Rigid Bodies - A collection of particles that do not move relative to each other. What forces are present with the.
 Momentum – the motion of mass  If an object is moving, it has momentum ▪ An object with lots of momentum will be hard to stop. ▪ An object with little.
Momentum.
Unbalanced Forces. Topic Overview A force is a push or a pull applied to an object. A net Force (F net ) is the sum of all the forces on an object (direction.
Work Booklet 2.4 page 17 Additional Review Exercise 1. A ball, A, of mass 2.0 kg and moving at 5.0 m/s strikes a glancing blow on a second ball, B, which.
Chapter 7 Linear Momentum. Objectives: The student will be able to: Apply the laws of conservation of momentum and energy to problems involving collisions.
Lecture 12: Collisions and Explosions l Momentum Examples! è Problem Solving è Collisions (elastic & inelastic) è Explosions.
Types of Collisions Elastic Two objects collide and bounce off each other Inelastic Two objects collide and stick together Explosion One object separates.
2D Collisions Physics 12. Clip of the day: Minutephysics: What is fire? gE
IB Physics 11 Mr. Jean December 9 th, The plan: Video clip of the day 2D collisions.
Today: (Ch. 7) Momentum and Impulse Conservation of Momentum Collision.
A –Level Physics: Further Mechanics- Inelastic and Elastic Collisions
Name 3 vectors and 3 scalars.
Physics 11 Mr. Jean May 9th, 2012.
(Constant acceleration)
Collisions © D Hoult 2010.
Collisions don’t just occur in one dimension, as we have been studying; they also occur in two or three dimensions.
Momentum And Impulse.
Elastic Collisions.
Two-Dimensional Collisions
Projectile motion.
Collisions in 2D.
Momentum.
Impulse and Momentum AP Physics C.
Momentum Chapter 1 Section 3.
Momentum:.
Conservation of Momentum in Two Dimensions
THIS IS JEOPARDY.
Day Topic: Conservation of Momentum
Aim: How do we solve collisions in two dimensions?
The height of the building
Elastic Collisions.
Lesson 4 HD Notes Answers
Momentum.
Impulse and Momentum Readings: Chapter 9.
Defining an explosion In an explosion, an internal impulse acts in order to propel the parts of a system (often a single object) into a variety of directions.
Conservation Laws Momentum and Impulse
Chapter 9: Linear Momentum and Collisions
Aim: How do we solve collisions in two dimensions?
Conservation Laws Conservation of Momentum I
Systems of Particles.
LAW OF CONSERVATION OF MOMENTUM
Work, Energy, Power.
Conservation Laws Conservation of Momentum II
Displacement, speed, velocity, acceleration and momentum
Presentation transcript:

Conservation Laws Conservation of Momentum II

Two Dimensional Explosions Momentum is conserved overall and it is also conserved in both the x and y directions. Use the same equations and techniques that we used in the previous lesson. Only this time solve everything twice. First solve the explosion in the x-direction using only x velocities. Then solve the explosion in the y-direction using only y velocities.

Example 1 A 5 kg mass explodes into three pieces. A 1 kg fragment moves in the -y direction at 6 m/s. A 2 kg fragment moves in the -x direction at 4 m/s. Determine the speed and direction of the third fragment. This splits into three fragments. We need the modify the equations. 5 kg Initially the problem begins with a 5 kg mass. It never tells you what the mass is originally doing. Assume the simplest case. It must be at rest , v0 = 0 . This means v0x = 0 and v0y = 0 Now take a look at what happens as a result of the explosion.

Example 1 A 5 kg mass explodes into three pieces. A 1 kg fragment moves in the -y direction at 6 m/s. A 2 kg fragment moves in the -x direction at 4 m/s. Determine the speed and direction of the third fragment. The second and third sentences tell us part of what happens during the explosion. They are not specific about what happens to the third fragment. 2 kg -4 m/s 2 kg 1 kg -6 m/s Before exploding the total mass was 5 kg. The mass of the third fragment must be 2 kg .

Example 1 Solve the x-direction Solve the y-direction 1 kg -6 m/s 2 kg A 5 kg mass explodes into three pieces. A 1 kg fragment moves in the -y direction at 6 m/s. A 2 kg fragment moves in the -x direction at 4 m/s. Determine the speed and direction of the third fragment. 1 kg -6 m/s 2 kg -4 m/s Solve the x-direction +3 m/s +4 m/s Solve the y-direction

Example 1 A 5 kg mass explodes into three pieces. A 1 kg fragment moves in the -y direction at 6 m/s. A 2 kg fragment moves in the -x direction at 4 m/s. Determine the speed and direction of the third fragment. Now Solve for the velocity and direction of the third fragment. 2 kg +4 m/s +3 m/s 5 m/s 37o Or, you could recognize this one as a 3-4-5 triangle and save some work. The calculations to the left would be necessary if the right triangle wasn’t easy.

Two Dimensional Collisions Momentum is conserved overall and it is also conserved in both the x and y directions. Use the same equations and techniques that we used in the previous lesson. Only this time solve everything twice. First solve the collision in the x-direction using only x velocities. Then solve the collision in the y-direction using only y velocities.

Example 2 First let’s imaging what the motion looks like 5 m/s 2 kg A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? First let’s imaging what the motion looks like 1 kg 2 kg 5 m/s

Example 2 First let’s imaging what the motion looks like 5 m/s 2 kg A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? First let’s imaging what the motion looks like 2 kg 5 m/s 1 kg

Example 2 First let’s imaging what the motion looks like 5 m/s 2 kg A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? First let’s imaging what the motion looks like 2 kg 5 m/s 1 kg

Example 2 First let’s imaging what the motion looks like 5 m/s 2 kg A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? First let’s imaging what the motion looks like 2 kg 5 m/s 1 kg

Example 2 First let’s imaging what the motion looks like ? m/s 2 kg A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? First let’s imaging what the motion looks like 2 kg ? m/s 1 kg 5 m/s

Example 2 First let’s imaging what the motion looks like ? m/s 2 kg A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? First let’s imaging what the motion looks like 2 kg ? m/s 1 kg 5 m/s © RJansen

Example 2 First let’s imaging what the motion looks like ? m/s 2 kg A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? First let’s imaging what the motion looks like 2 kg ? m/s 1 kg 5 m/s

Example 2 ? m/s First let’s imaging what the motion looks like 2 kg A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? 2 kg ? m/s First let’s imaging what the motion looks like We also only need to look at just the instant before the collision and the instant right after the collision. Why? It was constant velocity before and constant velocity after. 1 kg 5 m/s

Example 2 Let’s move this over to get some room for the equations. A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? Let’s move this over to get some room for the equations. 2 kg ? m/s 1 kg 5 m/s

Components Example 2 ? m/s I see vectors at angles. v1y  A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? 2 kg ? m/s 1 kg 5 m/s I see vectors at angles. v1x v1y  What is the secret first step to solve this problem? Components 37o 4 m/s 3 m/s We have a lot of information about the 1 kg mass (mass 2). Solving for the velocity components does not take much effort in this case. The 2 kg mass (mass 1) has unknown components. If we solve for these then we can find the overall velocity and angle of this mass.

Example 2 Solve in the x-direction ? m/s v1y  2 kg v1x 4 m/s 1 kg 37o A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? Solve in the x-direction 2 kg ? m/s 1 kg 5 m/s 37o 4 m/s 3 m/s v1x v1y 

Example 2 Solve in the x-direction 2 kg v1x 3 m/s 5 m/s 4 m/s 1 kg A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? Solve in the x-direction 2 kg 1 kg 5 m/s 4 m/s v1x 3 m/s

Example 2 Solve in the x-direction Now Solve in the y-direction ? m/s A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? Solve in the x-direction 2 kg ? m/s 1 kg 5 m/s 37o 4 m/s 3 m/s v1y  Now Solve in the y-direction

Example 2 Solve in the x-direction Now Solve in the y-direction A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? Solve in the x-direction 2 kg 1 kg 3 m/s v1y 1.5 m/s Now Solve in the y-direction Remember, down is negative

Example 2 Solve in the x-direction Now Solve in the y-direction ? m/s A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? Solve in the x-direction 1.5 m/s 2 kg ? m/s 1 kg 5 m/s 37o 4 m/s 3 m/s  Now Solve in the y-direction

Example 2 Solve in the x-direction Now Solve for v1 and  A 2 kg mass moving at 5 m/s in the +x-direction strikes a 1 kg ball at rest. The collision is slightly off center. After the collision the 1 kg ball moves with a speed of 5 m/s at an angle of 37o below the x-axis. What is the speed and direction of the 2 kg ball? Solve in the x-direction 2 kg ? m/s 1.5 m/s  3 m/s Now Solve for v1 and  Now Solve in the y-direction