Chapter 8 Impulse and Momentum
Units - kg m/s or sl ft/s THE LINEAR MOMENTUM • Momentum = mass times velocity • “Think of it as inertia in motion”
Units - N s or lb s AN IMPULSE • Collisions involve forces (there is a Dv). • Impulse = force times time.
AN IMPULSE CAUSES A CHANGE MOMENTUM Impulse = change in momentum
Case 1Increasing Momentum • Follow through • Examples: • Long Cannons • Driving a golf ball • Can you think of others?
Case 2Decreasing Momentum over a Long Time Examples: Rolling with the Punch Bungee Jumping Can you think of others? Warning – May be dangerous
Case 3Decreasing Momentum over a Short Time Examples: Boxing (leaning into punch) Head-on collisions Can you think of others?
BOUNCING There is a greater impulse with bouncing. Example: Pelton Wheel Pelton Wheel Water Sprinkler
Consider a hard ball and a clay ball that have +10 units of momentum each just before hitting a wall. • The clay ball sticks to the wall and the hard ball bounces off with -5 units of momentum. • Which delivered the most “punch” to the wall?
Initial momentum of the clay ball is 10. Final momentum of clay ball is 0. The change is 0 - 10 = - 10. It received - 10 impulse so it applied + 10 to the wall.
Initial momentum of the hard ball is 10. Final momentum of hard ball is - 5. The change is - 5 - 10 = - 15. It received - 15 impulse so it applied + 15 to the wall.
CONSERVATION OF LINEAR MOMENTUM Example: Rifle and bullet Demo - Rocket balloon Demo - Clackers Video - Cannon Shoot Video – Scooter Propulsion
Consider two objects, 1 and 2, and assume that no external forces are acting on the system composed of these two particles. • Impulse applied to object 1 • Impulse applied to object 2 • Apply Newton’s Third Law • Total impulse • applied • to system • or
Internal forces cannot cause a change in momentum of the system. • For conservation of momentum, the external forces must be zero.
IN COLLISIONS AND EXPLOSIONS • Collisions involve forces internal to colliding bodies. • Inelastic collisions - conserve momentum • Totally inelastic collisions - conserve momentum and objects stick together
A PERFECTLY ELASTIC COLLISION • Perfectly elastic collisions - conserve energy and momentum
Demos • Demo - Momentum balls • Demo - Small ball/large ball drop • Demo - Funny Balls
Head-On Totally Inelastic Collision Example • Let the mass of the truck be 20 times the mass of the car. • Using conservation of momentum, we get
Remember that the car and the truck exert equal but oppositely directed forces upon each other. • What about the drivers? • The truck driver undergoes the same acceleration as the truck, that is
The car driver undergoes the same acceleration as the car, that is The ratio of the magnitudes of these two accelerations is
Remember to use Newton’s Second Law to see the forces involved. • For the truck driver his mass times his acceleration gives • For the car driver his mass times his greater acceleration gives
Your danger is of the order of twenty times greater than that of the truck driver. TRUCKS. • Don’t mess with T
COEFFICIENT OF RESTITUTION For any collision between two bodies moving along a single straight line, the coefficient of restitution e is defined as
u’s are velocities before impact. v’s are velocities after impact. For perfectly elastic collisions e = 1. For inelastic collisions e < 1. For totally inelastic collisions e = 0.
Simple Examples of Head-On Collisions (Energy and Momentum are Both Conserved) Collision between two objects of the same mass. One mass is at rest. Collision between two objects. One at rest initially has twice the mass. Collision between two objects. One not at rest initially has twice the mass.
Example of Non-Head-On Collisions (Energy and Momentum are Both Conserved) Collision between two objects of the same mass. One mass is at rest. If you vector add the total momentum after collision, you get the total momentum before collision.
THE CENTER OF MASS The center of mass of an object of mass m is the single point that moves in the same way as a point mass would move when subjected to the same external forces that act on the object.
CENTER OF MASS ANDCENTER OF GRAVITY Center of mass - average position of mass Center of gravity - average position of weight . . Earth
Path of center of mass of a rotating object will be a straight line if no external forces act on the object.
Locating the Center of Gravity • Demo - Meterstick • Demo - Map of Texas • Demo - Balancing eagle • Demo - Curious George Center can be outside of the object. Examples: high jump and pole vaulting