Chap 6 Momentum and Collisions 6 1 Impulse momentum theorem In physics it is defined as Impulse F t unit N s In plain language it is the time total of a force it can change move things Remember Work is a distance total W Force displacement Baseball bat hockey stick ping pong racket Page 1 Average force Most of the time the force is not constant But you can always find an average for convenience Impulse is the area under the curve impulse F t For any given impulse you can find the average force giving an idea what can happen during that time period Momentum The linear momentum p of an object of mass m moving with a velocity v is defined as the product of the mass and the velocity p mv SI Units are kg m s Vector quantity the direction of the momentum is the same as the velocity s Page 2 Impulse momentum theorem F ma F m v f vi t F t mv f mvi Impulse Change in momentum Page 3 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 Example In a crash test a car of mass 1500 kg collides with a wall and rebounds as in Fig The initial and final velocities of the car are 15 and 2 6 m s respectively If the collision lasts for 0 15 s find a the impulse delivered on the car and b size and direction of average force exerted on the car Page 4 6 2 The principle of momentum conservation If there is an external force anything can happen If there is no external force they follow rules The forces between themselves are internal forces For Jane F21 t m1 v1f v1i For Fred F12 t m2 v2f v2i F21 F12 action reaction m1 v1f v1i m2 v2f v2i m1v1i m2v2i m1v1f m2v2f momentum is conserved Conservation of Momentum 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 Page 5 6 3 Collision in One Dimension Collision in physics two things come together and may or may not move apart Elastic collision no loss of kinetic energy the two colliding don t change shape like billiard balls Inelastic collision Completely inelastic collision Two stuck together after the collision The reason for different labels is convenience of calculations Momentum is conserved in all three cases Elastic collision usually happens to really solid things 1 momentum conserved pf total pi total 2 kinetic energy conserved KEf total KEi total Page 6 Completely inelastic collision stuck together after the collision m1v1i m2v2i m1v1f m2v2f v1f v2f vf Mechanical energy is NOT conserved here because sticking takes energy V 500 m s m1 0 02 kg m2 1 0 kg Sketches for Collision Problems Draw before and after sketches Label each object include the direction of velocity keep track of subscripts Page 7 Sketches for Perfectly Inelastic Collisions The objects stick together Include all the velocity directions The after collision combines the masses Example A ballistic pendulum is a device used to measure the speed of a fast moving projectile such as a bullet The bullet is fired into a large block of wood suspended from light wires The bullet is stopped by the block and the entire system swings up to a height h It is possible to obtain the initial speed of the bullet from this height h Mass of bullet 5 g Mass of pendulum 1 kg Height h 5 cm Find the initial speed of bullet Page 8 6 4 Glancing collision Old trick components v into vx and vy m1v1xi m2v2xi m1v1xf m2v2xf m1v1yi m2v2yi m1v1yf m2v2yf Momentum conservation works independently for the x and y directions just like in kinematics All types of collisions e g elastic apply here Page 9