Momentum Mass in Motion What do you think that means? Based on this description, what two things do you think affect momentum? 1
Momentum Inertia in motion Why are supertanker engines shut off 25 km from port? Why does a bus do better than a VW in collisions? p Usually kg Momentum = mass velocity mv Usually m/s Units- mass speed units So kg m/s Massive objects moving at high speed => large momentum Bill Nye Momentum Video-18min (kg*m) can also be written as N so N/s is another way of writing the units for momentum
Conservation of Momentum Momentum is a conserved quantity -for any closed, isolated system, the total momentum is the same before and after a collision or explosion. Σp i = Σp f **Must keep track of direction of velocity (+ or -)
Collisions & Explosions Elastic collision Objects bounce off each other Before After m 1 v 1 + m 2 v 2 = m 1 v 1 + m 2 v 2 Inelastic collision Objects stick together Before m 1 v 1 + m 2 v 2 = m 1+2 (v 1+2 ) Explosion After Object splits apart p of original object = p of all pieces added together
Elastic Collisions
Elastic Collisions
Inelastic Collisions
Inelastic Example p 1 + p 2 = p 1+2 m 1 v 1 + m 2 v 2 = m 1+2 (v 1+2 ) (4kg*6m/s) + (2kg*0m/s) = 6kg * v 1+2 And solve for V 1+2
Explosions B A Formula: Why 0? p Before = p After 0 = m a v a + m b v b 9
Explosion Example A B p a m = p b m = v = M a V a M b V b v = p = p = Total p After: OR you can set up like this
Problem Solving Steps Draw 2 diagrams of the system- before & after the collision Elastic: 2 objects 2 objects Inelastic: 2 objects 1 object Explosion: 1 object 2 objects Identify (+) & (-) directions Label all known masses & velocities Label m or v for unknowns Find momentum for all objects with p=mv Make equation: Σp i = Σp f Solve for unknown variable Reminders: p=0 if not moving If 1 object (inelastic/explosion) add both masses together
Bowling A 5-kg bowling ball moving east at 2 m/s strikes a stationary 1-kg bowling pin. after the head-on collision, the pin is moving east at 3 m/s. Determine the post collision velocity of the bowling ball. What type of collision? Try it in your notebook!! m 1 v 1 + m 2 v 2 = m 1 v 1 + m 2 v 2 12
Bowling A 5-kg bowling ball moving east at 2 m/s strikes a stationary 1-kg bowling pin. after the head-on collision, the pin is moving east at 3 m/s. Determine the post collision velocity of the bowling ball. m 1 v 1 + m 2 v 2 = m 1 v 1 + m 2 v 2 5kg(2m/s) + 1kg(0m/s) = 5kg(?) + 1kg(3m/s) 10 kg*m/s = 5kg(?) + 3kg*m/s 7 kg*m/s = 5kg(?) Velocity of bowling ball after collision = 1.4 m/s 13
Train Link A 500 kg train engine runs into a 2000 kg stationary box car. If the engine was traveling 10 mph before link up, how fast does the train move after? What type of collision is this? Momentum Before Momentum After p Before = p After m 1 v 1 + m 2 v 2 = m both (v both ) 500kg(10mph) + 2000kg(0mph) = 2500kg(v both ) V = 2 mph
Snowball Toss A 20 kg snowball is thrown at a 60 kg snowman at 10 km/h. If the snowball sticks to the snowman, how fast will the snowman move backwards? What type of collision is this? p 1 + p 2 = p 1+2 m 1 v 1 + m 2 v 2 = m 1+2 (v 1+2 ) + = * v 1+2
Two Astronauts Playing Catch Two astronauts are playing catch in space. What do you think will happen when one of them throws a ball? What type of scenario is this? Explosion! The astronaut and the ball will move away from each other. Astronaut + Ball = One object before 16
Two Astronauts Playing Catch Two astronauts, initially at rest, are playing catch in outer space with a 1 kg ball. One of the astronauts throws the ball at a velocity of 20 m/s. How fast is the astronaut moving after she throws the ball if she has a mass of 100 kg? Remember: Explosion is 1 object becoming two! p Before = p After 0 = m a v a + m b v b 0 = 100kg(v a ) + 1kg(20m/s) v a = -.2m/s 17
Think About It!!! Tennis Ball B Cannon A A cannonball with mass m b is fired from a cannon with mass m a with a speed of v a. How can I rearrange the formula to find the recoil speed of the gun, v a? Original Formula: 0 = m a v a + m b v b Rearrange it: m a v a = m b v b v a = (m b v b )/ m a 18
Changes in Momentum To cause a change in momentum, a force must be exerted on an object over a time interval.
Impulse Impulse (I) is the change in momentum. Since an impulse causes a change in momentum, mathematically, I = Δp OR Ft = mδv Units: N s or kg m/s Same direction as force being applied
Impulse, Force and Time Pads, cushions, air bags, and anything soft protect objects because they increase the time it takes to change an object s momentum The longer it takes to change momentum, the less force is applied to the object
Cannon Ball! F t = m Dv If two cannons shoot with the same amount of Force why is the speed of a cannon ball greater when fired from a longer cannon barrel?
Cannon Ball: Interaction Time F t = m Dv The longer cannon barrel gives the cannon ball a larger impulse and therefore more momentum. F acts for a longer time (Dt) to build up velocity (Dv). F Dt = m Dv
Impulse and Momentum F t = m Dv Impulse Momentum If a change in velocity (momentum) occurs over a short time, a large force must act. If that same change in velocity (momentum) occurs over an extended time, a small force must be acting.
Practice Problem Sand runoffs are provided on mountain highways to stop out of control vehicles. If a 2200 kg car traveling 26 m/s on a mountain road can be stopped in 21 s by driving into a sand runoff OR in 0.22 s if it hits the guardrail, what is it s change in momentum? What is the average force exerted on the vehicle in each of these stops? Givens: m=2200 kg v i =26 m/s v f =0 m/s Dv=-26 m/s Dt sand =21 s Dt rail =.22 s Ft Equation: mdv F F F F F F rail rail rail sand sand sand Work:.22s 2200kg 26 m s 57200kg m.22s 260,000N 21s 2200kg 26 m s 57200kg 21s 2723.8N m s s
Example If a 5 kg ball experiences a force and increases its velocity from 2 to 10 m/s, what is the change in the ball s momentum?
Example A golfer strikes a 0.06 kg ball (initially at rest) with a force of 280 N. If the ball and club are in contact for 0.015 s, what is the ball s final velocity?