MOMENTUM Expectations Title of your notes: MOMENTUM Expectations Calculate the impulse applied to, and momentum of a physical system Demonstrate and apply the laws of conservation of momentum in one dimension When you see this star…write the information down!
Stand in front of a 1000 kg truck moving at 1 m/s Suppose you were captured by an evil, crazy physics teacher. She gave you the following choice: Stand in front of a 1000 kg truck moving at 1 m/s Or Stand in front of a 1kg meatball moving 1000 m/s
What do you choose? What do you choose? The meatball is very dangerous! Beware! It isn’t very massive, but it’s moving very fast! Think about it; we’ll come back to it later…
Think in terms of sports… What is momentum? What is momentum? Think in terms of sports… Momentum can be thought of as “how difficult it is to stop a moving object”
p = mv Momentum depends on… Momentum depends on… Equation Alert: The little “p” is from the term progress defined as “the quantity of motion with which a body proceeds in a certain direction.” Momentum=(mass)(velocity)
Mrs. Lessner…you’re nuts! Wouldn’t their momentum be the same? Let’s compare the kinetic energy and the momentum of both objects… hmmm…which is worse? The meatball or the truck? Clearly KE and momentum are not the same! Write down the example I do on the board comparing the momentum of the two objects
Units for momentum problems Kg•m/s mass velocity
Conservation of Momentum Momentum isn’t created or destroyed in a given system. It may be transferred from one object to another. Only an outside or external force will change the total momentum
Conservation of Momentum What does that mean to me? The total momentum before a collision = the total momentum after a collision m1v1i = m2v2f The same applies for a “recoil” velocity
Conservation of Momentum Vocab Alert: Closed system: one not affected by external forces Isolated system: completely isolated from environment System: Portion of the universe focused on for study.
Conservation of Momentum Example: Conservation of Momentum Calculate the recoil velocity of a 4.0kg rifle that shoots a 0.05kg bullet at a speed of 280 m/s. Vfr = -3.5 m/s Because the rifle has a much larger mass, it’s velocity will be much smaller than the bullet
Impulse Impulse Product of net force and time Vector in direction of force An impulse causes a change in momentum Units: -N•s Why is there a negative sign?
Impulse Impulse Impulse = (Ft) Equation Alert: http://www.acs.psu.edu/drussell/
Impulse-Momentum Theorem Equation Alert: Ft = p Impulse = change in momentum – so a change in force over time, creates an impulse
Impulse-Momentum Theorem Ft = mv Impulse Momentum
Coming to a stop sign Coming to a stop sign Change momentum of car by applying brakes More force = less time More time = less force How does my change in momentum change in the two situations above? Or doesn’t it?
Increase time, thereby reducing force How do Airbags work? How do Airbags work? Increase time, thereby reducing force
Sports Science
Demonstration: Impulse-Momentum Two identical balls are dropped from the same height onto the floor. In case 1 the ball bounces back up, and in case 2 the ball sticks to the floor without bouncing. In which case is the impulse given to the ball by the floor the biggest? 1. Case 1 2. Case 2 3. The same The impulse-momentum theory says that the impulse that acts on an object is given by the change in the momentum of the object, and this change is proportional to the change in velocity. The ball that sticks has a velocity of downward to zero, but the velocity of the ball that bounces goes downward then upward. This change in momentum is greater and therefore has a greater impulse on it.
Example 1: Impulse Impulse A soccer ball (mass 0.425 kg), rolls toward an attacking midfielder at 6 m/s. The ball is shot toward the goal at a speed of 26 m/s. Given that the kick’s impact lasted for 0.008s, what was the average force on the ball?
Example 2: Impulse Impulse What average force must act on a 7.8 x 104 kg Boeing 737 to bring it from rest to a takeoff speed of 67 m/s in 40 s?
Skip #1 on your Guided Notes page for now. We’ll come back to it. Collisions Collisions Skip #1 on your Guided Notes page for now. We’ll come back to it.
Elastic Collisions Elastic Collisions An elastic collision is one where: Momentum is conserved. Kinetic energy is conserved The objects colliding aren’t deformed or smashed (Thus no kinetic energy is lost) Ex: billiard ball collisions Make sure everyone understands what “conserved” means
Inelastic Collisions Inelastic Collisions An inelastic collision is one where: Momentum is still conserved Kinetic energy is lost. The lost kinetic energy will be transformed into other energy types The objects often interlock and stick together May be deformed and mangled Main indicator is the lack of conservation of KE. Ex: car crash Make sure everyone understands what “conserved” means
Problem Solving Steps Go back to “#1…” in your Guided Notes. Draw a picture for the “initial” scenario Before the collision Draw a picture for the “final” scenario After the collision Write your Conservation of Momentum Equation based on your initial and final scenario Isolate the unknown & substitute values
Example: Collisions A 0.0050 kg bullet is fired at a velocity of 450 m/s from a 2.0 kg gun. What is the recoil velocity of the gun? (explosions are reverse collisions) Elastic or Inelastic? What is conserved: Momentum, KE or both?
𝑚 𝑏 𝑣 𝑏𝑖 + 𝑚 𝑔 𝑣 𝑔𝑖 = 𝑚 𝑏 𝑣 𝑏𝑓 + 𝑚 𝑔 𝑣 𝑔𝑓 A 0.0050 kg bullet is fired at a velocity of 450 m/s from a 2.0 kg gun. What is the recoil velocity of the gun? (explosions are reverse collisions) mb=0.0050kg vbf=450m/s mg=2.0kg vbi=0m/s vgi=0m/s Vgf in m/s Initial Final 𝑝 𝑖 = 𝑝 𝑓 𝑚 𝑏 𝑣 𝑏𝑖 + 𝑚 𝑔 𝑣 𝑔𝑖 = 𝑚 𝑏 𝑣 𝑏𝑓 + 𝑚 𝑔 𝑣 𝑔𝑓 0= 𝑚 𝑏 𝑣 𝑏𝑓 + 𝑚 𝑔 𝑣 𝑔𝑓 𝑣 𝑔𝑓 = − 𝑚 𝑏 𝑣 𝑏𝑓 𝑚 𝑔 𝑣 𝑔𝑓 = −0.0050𝑘𝑔×450 𝑚 𝑠 2.0𝑘𝑔 =-1.125m/s It’s not moving!
Example: Collisions A 1200 kg car is stopped at a traffic light when a 3500 kg truck moving at 8.4 m/s hits it from behind. The bumpers lock, and after the collision they both move at 4 m/s. Is this an elastic or inelastic collision?