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Momentum Momentum: the product of mass and velocity • Momentum is inertia in motion. • Ex: a dog running down the street • Equation: mv = p • p = momentum (kg*m/s) • m = mass (kg) • v = velocity (m/s)
A more massive object has more p than an object with less mass. • An object at rest has no p (v = 0) • If the p of an object changes, the m, v, or both MUST change. • If the v changes, then the object is accelerating • a produces F • The greater the F, the greater Δv • Which means a greater Δp
Check Your Understanding Which has more momentum, a dog running down the street or a large semi truck parked on the side of the road? • The running dog has momentum. The truck has no momentum because it is not even moving.
Check Your Understanding A 10 kg cart is rolling down the street at 10 m/s. What is the cart’s momentum? • p = ? m = 10 kg v = 10 m/s mv = p (10)(10) = p = 100 kg*m/s
Impulse • The F sustained for a longer period of time produces more ∆p. • This relationship of F to t is called impulse. Impulse: product of force and time interval during which the force acts. • Impulse does NOT change in a collision • Ex: a car colliding with another car • Equation: J = F∆t • J = impulse (N*s) • F = force (N) • ∆t = time (s)
Impulse is equal to the change in momentum. • J = Δp • In collisions, the amount of damage depends on several things. • One is the hardness of surfaces that connect. • Two softer, more malleable objects will do less damage than two harder, more rigid objects.
J does not change if an egg hits a more or less malleable surface b/c the object’s change in momentum would be the same either way. • J is the same for both • the only thing that changes is the time interval of impact. • As the t increases, the F decreases. • Ex: car crash with and without airbags, landing on the ground with bent knees vs. straight legged
Check Your Understanding Why is falling on a floor with more give (like a big fluffy pillow) less dangerous than falling on a floor with less give (like concrete or brick)? • Because the floor with more give allows a greater time for an object to come to rest. A greater time for a change in momentum results in less force.
Check Your Understanding When a dish falls, will the impulse be less if it lands on carpet than if it lands on hard floor? • No. The impulse would be the same for either surface because the same momentum change occurs for each. It is the force that is less for the dish on the carpet because of the greater time of momentum change.
Conservation of Momentum Law of Conservation of Momentum: In the absence of an external force, the momentum of a system remains unchanged. • In the absence of an external force, the momentum of a system remains unchanged. • Ex: a gun will recoil when fired b/c the momentum of the gun and bullet together before the shot should equal the total momentum of the bullet and the gun after they have been shot.
When a cannon is fired, according to Newton’s 3rd, the ball has an equal but opposite force to the cannon. • Same thing with p (within the system of the cannon and the ball)…the overall p before and after do not change…ignoring friction. • Remember p is vector quantity (magnitude AND direction) • If no net force or net J act on a system, the momentum of that system cannot be changed.
Check Your Understanding When fighting fires, a firefighter must use great caution to hold a hose which emits large amounts of water at high speeds. Why would such a task be difficult? • The hose is pushing lots of water (large mass) forward at a high speed. This means the water has a large forward momentum. In turn, the hose must have an equally large backwards momentum, making it difficult for the firefighters to manage.
Check Your Understanding A bomb is sitting at rest on the ground. It explodes into 3 pieces with a mass of 5 kg, one moving at a speed of 3 m/s east, the other moving at a speed of 5 m/s northwest, and the last moving at a speed of 4 m/s south. What is the total momentum of all 3 pieces after the explosion? • Zero! The momentum before equals the momentum after.
Collisions • The collision of objects clearly shows the conservation of p. Net momentum before collision = Net momentum after collision • Two main types of collisions • Elastic and inelastic
Elastic Collisions Elastic collision: When objects collide without being permanently deformed or without generating heat • The momentum from the first object is transferred to the second object (or vice versa). • Ex: billiard balls (pool); Newton’s Cradle
Inelastic Collisions Inelastic collisions: When colliding objects become entangled or coupled together, thereby generating heat or disfigurement • The net p before the collision equals the net p after the collision • Ex: car crashes, sports, bumper cars