#### Transcript What do you know about momentum?

What do you know about momentum? Which has more momentum? A hummingbird zipping down the street (v = 1 m/s)? A bus stopped at a stop sign? A bus barreling down the road (v = 10 m/s)? A hummingbird hovering at a feeder? What does momentum depend on? Newton’s Cradle link Definition Linear momentum (p) is defined as the product of an object’s mass and its velocity. p=mv Momentum is a vector quantity and the direction of the momentum vector is the same as the velocity vector. The units for momentum are Notice that in all the examples the typically kg-m/s mass is multiplied Other acceptable units: kg*mi/hr, kg*km/hr, and g*cm/s by the velocity. Since Momentum is a Vector Quantity.... ….You must include the direction for the velocity vector in the calculation Mass = 10 kg v = 10 m/s P = 100 kgxm/s Mass = 10 kg v = 10 m/s P = -100 kgxm/s Use the established sign convention: right & up is positive while left & down is negative. Changing Momentum To change momentum, either mass or velocity changes, but usually it is caused by a change in velocity: Δp = mvf-mvi Or Δp =m (vf –vi)...if same mass m = 10 kg v = 10 m/s pi = mvi= 0 pf = mvf = 100 kg·m/s Δp = 10 kg ( 10 m/s – 0) = 100 kg ·m/s Changing DIRECTION changes momentum (since it is a change in velocity). m = 10 kg v = 10 m/s m = 10 kg v = 10 m/s pi = mvi = 100 kg·m/s pf = mvf = 100 kg·m/s Δp = -100 kg·m/s – 100 kg ·m/s Δp = -200 kg·m/s Remember: Subtracting vectors is adding a negative vector Rebounding causes a greater change in momentum than stopping Bouncing off an object is known as rebounding. (J) Impulse = changing momentum (p) To change an objects velocity, it is necessary to apply a force against its motion for a given period of time. The more momentum, the greater the force needed to stop the object or the force will need to be applied for a greater time period. Impulse –force applied through time Formula: J =F Δt Unit: N s Force and Momentum Youtube Remember, an unbalanced force causes acceleration. F = ma Remember, acceleration is a change in velocity. a = v/ t So: F = m v / t Therefore, a force acting for a given amount of time will change an object's momentum. F t = m v If the force acts opposite the object's motion, it slows the object down. If a force acts in the same direction as the object's motion, it speeds the object up. Impulse-Momentum Theorem Since a force applied through time changes momentum, Impulse is a change in momentum, and is therefore a vector quantity. J=Δp F * Δt = mvf-mvi Or F * Δt =m (vf –vi) ...if same mass Notice: If I = p, then the units equal each other, and can be interchanged, ie. Kg-m/s = N s Applying Theorem Greatest velocity change? Greatest acceleration? Greatest momentum change? Greatest Impulse? Case B (-28 m/s – 30 m/s) = - 58 m/s Case B, acceleration depends on velocity Case B, momentum depends on velocity Case B, impulse depends on change in momentum Why do we use airbags in cars? Airbags apply less force over a greater time when there is a change in momentum. p = F t A given impulse... say a car going from 60 mph to 0... can be achieved by: p = F t = F t =BIG FORCE Crash test short time = small force longer time Using the ImpulseMomentum Theorem: A 1400-kg car traveling west with a family of crash test dummies has a velocity of 15 m/s when it collides with a utility pole and is brought to rest in 0.30 seconds. Find the magnitude of the net force exerted on the car during the collision. pi=mvi=1400 kg (15 m/s) pf=mvf=0 p = F t 1400 kg (0-15 m/s) = F (0.30 s) F = 7.0 x 104 N (to the east) Conservation of Momentum and Collisions So long as the unbalanced forces exerted on a system are internal to the system… meaning they’re exerted by other parts of the system, the momentum of a system is conserved (will not change). Conservation of Momentum Total initial momentum = total final momentum pi = p f m1 v1i + m2 v2i = m1 v1f + m2 v2f Linear momentum is conserved when the net force on an isolated system is zero. Linear= straight line or curves but NOT repeat the motion Isolated= internal forces only—NO friction System= all initial interacting objects/particles Which of the following is an example of an isolated system? 1. Two cars collide on a gravel roadway on which frictional forces are large. 2. Hans Full is doing the annual vacuuming. Hans is pushing the Hoover vacuum cleaner across the living room carpet. * 3. Two air track gliders collide on a friction-free air track. COLLISIONS Perfectly ELASTIC Collisions – 2 objects collide and bounce off of each other Total Momentum and total kinetic energy is +v when object conserved (as long as moves right, -v when object system is isolated) moves left m1 v1i + m2 v2i = m1 v1f + m2 v2f Collisions applet Car Rear Ends Truck The animation below portrays the elastic collision between a 1000-kg car and a 3000-kg truck. In this elastic collision, the total kinetic energy in the system is conserved. Collisions Perfectly Inelastic Collisions – the objects stick together after impact; Kinetic energy is not conserved since some of the energy is converted to sound, heat and objects are deformed. Total momentum is still conserved Inelastic Collisions You are hovering next to the space and your buddy of equal mass who is moving 4 m/s (with respect to the ship) bumps into you. If she holds onto you, then how fast do the two of you move after the collision? Since there is twice as much mass in motion after the collision, it must be moving at one-half the velocity 2m/s. m1 v1i + m2 v2i = ( m1 + m2)vf Little Fish in Motion is Caught by Big Fish Big Fish in Motion Catches Little Fish The animation below portrays the collision between a 1.0-kg cart and a 2-kg dropped brick. In the collision between the cart and the dropped brick, total system momentum is conserved. The momentum lost by the loaded cart (40 kg*cm/s) is gained by the dropped brick. In an EXPLOSION, two objects at the same velocity (usually at rest and therefore 0 m/s) separate into two objects at separate velocities, each with the same momentum. Pfinal bullet = mbvb Pfinal man/gun = mmgvmg Pinitial = Pfinal ( m1 + m2) v0i = m1v1f + m2v2f m1v1f = m2v2f Since the initial momentum is zero, so is the final, with the two vectors canceling each other out. Explosions A 100 kg cannon recoils 1 m/s when firing a 5 kg cannon ball. What is the velocity of the cannon ball fired? ( m1 + m2) 0vi = m1v1f + m2v2f m1v1f = m2v2f 100 kg (1 m/s) = (5 kg) v2f V2f = 50 m/s