chapter 8 linear momentum and collisions - …users.tamuk.edu/karna/physics/cpich8.pdf ·...
TRANSCRIPT
![Page 1: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/1.jpg)
Chapter 8 LINEAR MOMENTUM AND COLLISIONS
![Page 2: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/2.jpg)
• Linear Momentum
• Momentum and Newton’s Second Law
• Impulse
• Conservation of Linear Momentum
• Inelastic Collisions
• Elastic Collisions
• Center of Mass
• Systems with Changing Mass: Rocket Propulsion
Linear Momentum
![Page 3: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/3.jpg)
Change in momentum:
(a) mv
(b) 2mv
Momentum and Newton’s Second Law Newton’s
second law, as we wrote it before:
![Page 4: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/4.jpg)
Impulse Impulse is a vector, in the same direction as the average force.
![Page 5: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/5.jpg)
Therefore, the same change in momentum may be produced by a large force
acting for a short time, or by a smaller force acting for a longer time.
Conservation of Linear Momentum The net force acting on an object is the rate of change of its momentum:
![Page 6: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/6.jpg)
Conservation of Linear Momentum
![Page 7: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/7.jpg)
![Page 8: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/8.jpg)
An example of internal forces moving components of a system:
![Page 9: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/9.jpg)
Inelastic Collisions Collision: two objects striking one another Time of collision is short enough that external forces
may be ignored
Inelastic collision: momentum is conserved but kinetic energy is not Completely inelastic
collision: objects stick together afterwards
Inelastic Collisions A completely inelastic collision:
![Page 10: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/10.jpg)
Inelastic Collisions
Solving for the final momentum in terms of the initial momenta and masses:
![Page 11: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/11.jpg)
Ballistic pendulum:
the height h can be found using conservation of mechanical energy after the object is embedded in the block.
![Page 12: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/12.jpg)
For collisions in two dimensions, conservation of momentum is applied separately along each axis:
![Page 13: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/13.jpg)
Elastic Collisions In elastic collisions, both kinetic energy and momentum are conserved.
One-dimensional elastic collision:
![Page 14: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/14.jpg)
Elastic Collisions We have two equations
(conservation of momentum and conservation of
kinetic energy) and two unknowns (the final speeds). Solving for the final speeds:
![Page 15: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/15.jpg)
Elastic Collisions Two-dimensional collisions can only be solved if some of the final
information is known, such as the final velocity of one object:
![Page 16: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/16.jpg)
Center of Mass The center of mass of a system is the point where the system
can be balanced in a uniform gravitational field.
![Page 17: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/17.jpg)
![Page 18: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/18.jpg)
The center of mass need not be within the object:
![Page 19: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/19.jpg)
![Page 20: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/20.jpg)
The total mass multiplied by the acceleration of the center of mass is equal to the net external force:
The center of mass accelerates just as though it were
a point particle of mass M acted on by
![Page 21: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/21.jpg)
Systems with Changing Mass: Rocket Propulsion If a mass of fuel Δm is
ejected from a rocket with speed v, the change in momentum of the rocket is:
The force, or thrust, is
![Page 22: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/22.jpg)
Summary
• Momentum is conserved if the net external force is zero
• Internal forces within a system always sum to zero
• In collision, assume external forces can be ignored
• Inelastic collision: kinetic energy is not conserved
• Completely inelastic collision: the objects stick together afterward
![Page 23: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/23.jpg)
• A one-dimensional collision takes place along a line
• In two dimensions, conservation of momentum is applied separately to each
• Elastic collision: kinetic energy is conserved
• Center of mass:
![Page 24: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/24.jpg)
• Motion of center of mass:
• Rocket propulsion:
![Page 25: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/25.jpg)
An elastic one-dimensional two-object collision. Momentum and internal kinetic energy are conserved.
• An inelastic one-dimensional two-object collision. Momentum is conserved, but internal kinetic energy is not conserved.
(a) Two objects of equal mass initially head directly toward one another at the same speed.
(b) The objects stick together (a perfectly inelastic collision), and so their final velocity is zero. The internal kinetic energy of the system changes in any inelastic collision and is reduced to zero in this example.
![Page 26: Chapter 8 LINEAR MOMENTUM AND COLLISIONS - …users.tamuk.edu/karna/physics/CPICh8.pdf · Conservation of Linear Momentum The net force acting on an object is the rate of change of](https://reader034.vdocuments.us/reader034/viewer/2022051106/5afcef8f7f8b9a434e8cd2b4/html5/thumbnails/26.jpg)
• A two-dimensional collision with the coordinate system chosen so that m2 is initially at rest and v1 is parallel to the x -axis. This coordinate system is sometimes called the laboratory coordinate system, because many scattering experiments have a target that is stationary in the laboratory, while particles are scattered from it to determine the particles that make-up the target and how they are bound together. The particles may not be observed directly, but their initial and final velocities are.