# SJSU PHYS 2A - Momentum and Collisions (57 pages)

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## Momentum and Collisions

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- Pages:
- 57
- School:
- San Jose State University
- Course:
- Phys 2a - Fundamentals of Physics

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Chapter 6 Momentum and Collisions Introduction Last Chapter W F d E no external nc force means conservation of energy F ma m v t mv t no external force means mv is conserved What is mv Momentum r The linear momentum p of an object ofr mass m moving with a velocity v is defined as the product of rthe mass and the velocity r p mv SI Units are kg m s Vector quantity the direction of the momentum is the same as the velocity s More About Momentum Momentum components px m vx and py m vy Applies to two dimensional motion Momentum is related to kinetic energy p2 KE 2m Impulse In order to change the momentum of an object a force must be applied The time rate of change of momentum of an object is equal to the net force acting on it r p m v f v i r Fnet t t Gives an alternative statement of Newton s second law Impulse cont When a single constant force acts on the object there is an impulse delivered to the object r r I F t r I is defined as the impulse Vector quantity the direction is the same as the direction of the force Impulse Momentum Theorem The theorem states that the impulse acting on the object is equal to the change in momentum of rther object r r r I F t p mv f mv i If the force is not constant use the average force applied Average Force in Impulse The average force can be thought of as the constant force that would give the same impulse to the object in the time interval as the actual time varying force gives in the interval Average Force cont The impulse imparted by a force during the time interval t is equal to the area under the force time graph from the beginning to the end of the time interval Or the impulse is equal to the average force rmultiplied r by the time interval Fav t p Example Impulse Examples Example racquet tension Racquetball goes over 190 mph and tennis goes over 160 mph How tight should you string your racquet to get to that speed Tighter better Kung Fu punch Keep the fist out Impulse Applied to Auto Collisions The most important factor is the collision time or the time it takes the person to come to a rest This will reduce the chance of dying in a car crash Ways to increase the time Seat belts Air bags Typical Collision Values For a 75 kg person traveling at 27 m s and coming to stop in 0 010 s F 2 0 x 105 N a 280 g Almost certainly fatal Survival Increase time Seat belt Restrain people so it takes more time for them to stop New time is about 0 15 seconds Air Bags The air bag increases the time of the collision It will also absorb some of the energy from the body It will spread out the area of contact Decreases the pressure Helps prevent penetration wounds Example momentum impulse light Conservation of Momentum Momentum in an isolated system in which a collision occurs is conserved A collision may be the result of physical contact between two objects Contact may also arise from the electrostatic interactions of the electrons in the surface atoms of the bodies An isolated system will have not external forces Conservation of Momentum cont The principle of conservation of momentum states when no external forces act on a system consisting of two objects that collide with each other the total momentum of the system remains constant in time Specifically the total momentum before the collision will equal the total momentum after the collision Conservation of Momentum Example The momentum of each object will change The total momentum of the system remains constant Forces in a Collision The force with which object 1 acts on object 2 is equal and opposite to the force with which object 2 acts on object 1 Impulses are also equal and opposite For the whole system I 0 Don t have to worry about F or I Conservation of Momentum cont Mathematically r r r r m1v1i m2 v2i m1v1f m2 v2f Momentum is conserved for the system of objects The system includes all the objects interacting with each other Assumes only internal forces are acting during the collision Can be generalized to any number of objects Notes About A System Remember conservation of momentum applies to the system You must define the isolated system Examples Types of Collisions Momentum is conserved in any collision Inelastic collisions Kinetic energy is not conserved Some of the kinetic energy is converted into other types of energy such as heat sound work to permanently deform an object Perfectly inelastic collisions occur when the objects stick together Not all of the KE is necessarily lost More Types of Collisions Elastic collision Both momentum and kinetic energy are conserved Actual collisions Most collisions fall between elastic and perfectly inelastic collisions Inelastic Collisions When two objects stick together after the collision they have undergone a perfectly inelastic collision Conservation of momentum becomes m1v 1i m2 v 2i m1 m2 v f About Collisions Momentum is a vector quantity Direction is important Be sure to have the correct signs More About Elastic Collisions Both momentum and kinetic energy are conserved Typically have two unknowns m1v 1i m2 v 2i m1v 1f m2 v 2 f 1 1 1 1 2 2 2 2 m1v 1i m2 v 2i m1v 1f m2 v 2 f 2 2 2 2 Solve the equations simultaneously Elastic Collisions cont A simpler equation can be used in place of the KE equation v1i v2i v1 f v2 f Examples elastic Elastic 2 in 1 out possible Summary of Types of Collisions In an elastic collision both momentum and kinetic energy are conserved In an inelastic collision momentum is conserved but kinetic energy is not In a perfectly inelastic collision momentum is conserved kinetic energy is not and the two objects stick together after the collision so their final velocities are the same Problem Solving for One Dimensional Collisions Coordinates Set up a coordinate axis and define the velocities with respect to this axis It is convenient to make your axis coincide with one of the initial velocities Diagram In your sketch draw all the velocity vectors and label the velocities and the masses Problem Solving for One Dimensional Collisions 2 Conservation of Momentum Write a general expression for the total momentum of the system before and after the collision Equate the two total momentum expressions Fill in the known values Problem Solving for One Dimensional Collisions 3 Conservation of Energy If the collision is elastic write a second equation for conservation of KE or the alternative equation This only applies to perfectly elastic collisions Solve the resulting equations simultaneously Sketches for Collision Problems Draw before and after

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