Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 25-29.

Slides:



Advertisements
Similar presentations
Problem of the Day An 1800 kg car stopped at a traffic light is struck from the rear by a 900 kg car, and the two become entangled, moving along the same.
Advertisements

Halliday/Resnick/Walker Fundamentals of Physics 8th edition
Momentum Momentum is conserved – even in collisions with energy loss. Collisions Center of mass Impulse Chapter 9: Linear Momentum and Collisions Reading.
Linear Momentum Vectors again.
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.
AP Physics Review Ch 7 – Impulse and Momentum
Chapter 7 Impulse and Momentum.
Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 18.
Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 28.
Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 25, 26.
Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 27, 28.
Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 19.
Instructor: Dr. Tatiana Erukhimova
Chapter 6 Momentum and Collisions. Momentum Definition: Important because it is CONSERVED proof: Since F 12 =-F 21, for isolated particles never changes!
Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 29.
Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 27.
Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 23.
Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 17.
Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 26.
Fri. Feb. 25th1 PHSX213 class Class stuff –Questions ? Conservation of Linear Momentum Collision terminology Collisions.
Ch. 8 Momentum and its conservation
Collisions and Momentum
Momentum Chapter 6. Momentum ► Related to inertia, not the same. ► Symbol is p ► p=mv ► Units of kgm/s ► What is the momentum of a 75kg rock rolling at.
Momentum is a Momentum vectors Impulse Defined as a Impulse is.
Momentum, Impulse, and Collisions
Physics 215 – Fall 2014Lecture Welcome back to Physics 215 Today’s agenda: More on momentum, collisions Kinetic and potential energy Potential energy.
Momentum and Collisions
Today: Momentum – chapter 9 11/03 Finish momentum & review for exam 11/8 Exam 2 (5 – 8) 11/10 Rotation 11/15 Gravity 11/17 Waves & Sound 11/22 Temperature.
1 PPMF102– Lecture 3 Linear Momentum. 2 Linear momentum (p) Linear momentum = mass x velocity Linear momentum = mass x velocity p = mv p = mv SI unit:
Chapter 6 Momentum and Impulse
Chapter 6 Momentum and Impulse. Momentum The product of an object’s mass and velocity: p = mv Momentum, p, and velocity, v, are vector quantities, meaning.
Reading Quiz - Momentum
Chapter 9 - Collisions Momentum and force Conservation of momentum
Chapter 7 Impulse and Momentum. 7.1 The Impulse-Momentum Theorem DEFINITION OF IMPULSE The impulse of a force is the product of the average force and.
Momentum, impulse, and collisions Chapter 8 Sections 1-5.
MOMENTUM AND COLLISIONS. Momentum is the product of the mass and velocity of a body. Momentum is a vector quantity that has the same direction as the.
Physics 218 Lecture 15: Momentum Alexei Safonov.
Momentum and Collisions Linear Momentum The linear momentum of a particle or an object that can be modeled as a particle of mass m moving with a velocity.
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.
Linear Momentum Problems MC Questions Linear Momentum 07 LH.
Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 30, 31, 32.
Lecture 13: Momentum. Questions of Yesterday 1) A mass with speed v hits a horizontal spring and compresses it a distance d. If the the speed of the mass.
Linear Momentum. 5-1 Linear Momentum Linear Momentum, p – defined as mass x velocity The unit is kgm/s A quantity used in collisions So a small object.
Lecture 14: Collisions & Momentum. Questions of Yesterday A 50-kg object is traveling with a speed of 100 m/s and a 100-kg object is traveling at a speed.
Momentum Momentum is conserved – even in collisions with energy loss due to friction/deformation. Impulse Chapter 9: Linear Momentum and Collisions Reading.
Phys211C8 p1 Momentum everyday connotations? physical meaning the “true” measure of motion (what changes in response to applied forces) Momentum (specifically.
Physics 1D03 - Lecture 26 Collisions Conservation of Momentum Elastic and inelastic collisions.
Momentum Chapter 6. Momentum ► Related to inertia, not the same. ► Symbol is p ► p=mv ► Units of kgm/s 1. What is the momentum of a 75kg rock rolling.
Momentum & Impulse Day #1: Introduction HW #7. Momentum & Collisions: Define Momentum: Momentum, p, is defined as the product of mass and velocity. Units:
Momentum, Impulses, and Collisions. A. Background Information 1.Momentum of an object is anything that has inertia and is moving a. It is based on an.
Instructor: Dr. Tatiana Erukhimova
Chapter 7 Impulse and Momentum.
Linear Momentum and Collisions
Chapter 7 Impulse and Momentum.
Aim: How do we solve collisions in two dimensions?
Instructor: Dr. Tatiana Erukhimova
Instructor: Dr. Tatiana Erukhimova
Instructor: Dr. Tatiana Erukhimova
Chapter 7 Impulse and Momentum.
Chapter 7 Impulse and Momentum.
Momentum and Collisions
Chapter 9: Linear Momentum and Collisions
Systems of Particles.
Lesson 10: Conservation of Momentum
APPC Unit 7: Momentum and Impulse
Instructor: Dr. Tatiana Erukhimova
Collisions and Momentum
Instructor: Dr. Tatiana Erukhimova
Presentation transcript:

Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 25-29

Center of Mass

Problem 5 from handout Find the position of the center of mass of the system of the sun and Jupiter. (Since Jupiter is more massive than the rest of the planets put together, this is essentially the position of the center of mass of the solar system.) Does the center of mass lie inside or outside the sun?

Motion of the Center of Mass

The center of mass of a system moves as if all of the mass of the system were concentrated at that point and as if all of the forces were acting at that point There is only the external forces that affect the motion of the center of mass ( ) Only external forces affect the motion of the center of mass

Momentum is a vector! Vector equation!

If

Conservation of Momentum If there is no external force on a system, then the total momentum of the system is a constant

True in X and Y directions separately!

Problem Solving For Conservation of Momentum problems: 1.BEFORE and AFTER 2.Do X and Y Separately

Before X Y

After Y X

Inelastic collision A collision in which the total kinetic energy after the collision is not equal to the kinetic energy before the collision is called an inelastic collision. A B BEFORE AFTER A B V after ?

Perfectly elastic collision A collision in which the total kinetic energy after the collision is the same than that before the collision is called an elastic collision. A B

A block of mass m is moving along x axis with a velocity of V 0. It collides with a block of mass M, initially at rest. 1) What is the change in kinetic energy of the system of two balls: a) if the collision is perfectly elastic; b) if the collision is perfectly inelastic (balls stick together after collision). 2) For m = M = m 0, find the velocity of each ball after a perfectly elastic collision.

Problem 4 p.200 In a nuclear collision an incoming proton has initial velocity of magnitude m/s. It collides with another proton, initially at rest. After the collision one proton goes off at 37 0 to the x axis. If the collision is perfectly elastic, find the velocities of the two protons after the collision.

The ballistic pendulum

“Famous Problem” from the book

A cannon is mounted on top of a narrow wall: There is no friction between the wall and the cannon. The cannon fires a cannon ball with a horizontal velocity v 0 =200 m/s. The cannon has mass 100 kg and the ball mass 10 kg. The height of the wall is 9.8 m. Find the final positions of the cannon and the cannon ball. Problem 5 p. 200

Quiz A block of mass m is sliding on a frictionless table with velocity v 0. It explodes into two pieces, one with mass m/3. The light piece flies off horizontally, perpendicular to the original direction of motion, with velocity 2v 0. Find as many equations as you need to find the velocity of the heavy piece.

You are standing on a frictionless surface. Some idiot throws a rock at you which you catch. In terms of your mass, the rock’s mass and the rock’s velocity find your position as a function of time after you catch the rock. Quiz

Impulse Changes in a particle’s momentum are due to impulse, which depends on the time over which the net force acts.

Impulse Suppose you throw a ball with a mass of 0.4 kg against a brick wall. It hits the wall moving horizontally to the left at 30 m/s and rebounds horizontally to the right at 20 m/s. a) Find the impulse of the net force on the ball during its collision with the wall. b) If the ball is in contact with the wall for s, find the average horizontal force that the wall exerts on the ball during the impact.

Quiz A small car weighing m 1 is traveling due north when it collides with a pick-up truck weighting m 2 which was traveling due east. After the collision the two vehicles move off together at an angle θ north of east. The driver of the car claimed that the truck driver was at fault because he was exceeding the speed limit, going with a velocity v 1. If this were true, what was the car’s initial velocity?

Polar coordinates

Have a great day! Hw: Chapter 12 problems and exercises Reading: Chapters 12, 13