Momentum & Collisions Chapter 6 Tbone video- momentum

ASTRONAUT Edward H. White II floats in the zero gravity of space ASTRONAUT Edward H. White II floats in the zero gravity of space. By firing the gas-powered gun, he gains momentum and maneuverability. Credit: NASA

Momentum Have you ever coasted down a hill on a bike? Maybe, you got to sled down a hill when we had the snow? What happened as you went down hill? What about when you tried to stop? Have you ever doubled up to go down a water slide? Why? Bike crashes on teacher tube?

Momentum Momentum means you are on the move and it’s going to take some effort to stop! It’s Mass in MOTION Is a vector quantity defined as the product of an object’s mass and velocity

Momentum Momentum is the product of the objects’ mass x it’s velocity The amount of momentum that an object has is dependent on two variables: how much stuff is moving and how fast the stuff is moving. Momentum is the product of the objects’ mass x it’s velocity p = mv where (kg· m/s) p = momentum m = mass in kg v = velocity in m/s

6A A 2250 kg pickup truck has a velocity of 25 m/s to the east. What is the momentum of the truck? P=mv Practice 6a 1-3

IMPULSE Impulse J is a force F acting for a small time interval Dt. F J = F Dt

Impulse-Momentum Theorem What does it take to change an object’s momentum? Force Force= change in momentum/ time interval A change in momentum takes force and time Change in momentum = Impulse (Ft) Product of the force and the time over which it acts on the object F t = p where F = Force t = time that the force is exerted F t = p = mvf –mvi

Impulse Can a small force acting for a long time produce the same change in momentum as a large force acting for a short time? Yes This is why follow through is so important in sports. When a batter hits the ball, the ball will have a higher momentum if the batter follows through. Why? the bat is in contact with the ball for a long time.

Sample 6B A 1400 kg car moving westward with a velocity of 15 m/s collides with a utility pole and is brought to rest in 0.30s. Find the magnitude of the force exerted on the car during the collision. F t = p = mvf –mvi Practice 6B 1-3 Workbook 1,2,7

Stopping Time How far do you have to be behind a car when following it? Why? Who determines this? (one car length, so you have time to stop, engineers) Stopping distances depend on the impulse-momentum theorem Which of these trucks has more momentum? Which will require more stopping time?

Stopping Distance the 2 trucks are the same, but one is loaded with bricks so that it has 2x the mass. Both are going 48 km/h The truck hauling a load has 2x the mass of the other truck. The stopping time takes 2x longer for the loaded truck than for the unloaded truck The stopping distance is 2x greater for the loaded truck

Stopping Time The trucks time period is 2x as great while it’s acceleration is ½ as much (F-ma). Why? Because X=vi∆t + ½ a ∆t2 The truck’s stopping distance is 4x as great as the car’s Practice 6C 1-3 Use info from this sample for #1 and #3 section review

Sample 6C A 2250 kg car traveling to the west slows down uniformly from 20 m/s to 5 m/s. How long does it take the car to decelerate if the force on the car is 8450 N to the east? How far does the car travel during the deceleration? F t = p = mvf –mvi x? F  t? x= ½ (vi+vf) t

Change in momentum What would happen if the egg hit the wall? Why did the egg not break when it hit the sheet? What happens if a change in momentum occurs over a longer period of time? (requires less force) Think about the nets that are used to catch people by firefighters The sheet extended the time of collision Momentum video Egg toss or video Sec Review 1-5 The change in momentum is the same But the blanket ‘gives way’ and extends the time of collision A longer time requires less force to achieve the same change in momentum. The force on the person is less hen hitting the blanket than when hitting the ground. The force on the egg is smaller so it doesn’t break

Riding the Punch

Conservation of Momentum We have 2 soccer balls. One is stationary while the other is moving. Assume balls are not affected by friction and don’t rotate before or after the collision Before the collision what is the momentum of Ball B? Zero Ball B gains momentum when ball A collides with it.. If momentum is conserved, what is the momentum of Ball A? equal to the momentum that ball B gains Ball A and B’s momentum aren’t constant, but the total momentum is.

Conservation of Momentum Ball A and B’s momentum aren’t constant, but the total momentum is. Law of Conservation of Momentum Total initial momentum=total final momentum m1v1i + m2v2i =m1v1f + m2v2f Law of Conservation of momentum the total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects

Momentum Conservation Conserved means ‘constant’ or ‘not changing’ For any collision in an isolated system, momentum is conserved All objects that are involved in the interaction must be included Momentum is conserved for objects pushing away from each other Forces in REAL collisions are not constant They change throughout the collision, even though overall they are conserved

Momentum conservation Imagine you are standing at rest and then jump up, leaving the ground with velocity v. Your momentum is not conserved – before the jump it was zero and it became mv as you rose. The TOTAL momentum however, remains constant if you include Earth in your analysis. If your momentum is 60 N upward then earth must have a corresponding momentum of 60 N downward.

6D 6D A 76 kg boater, initially at rest in a stationary boat, steps out of the boat onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right, what is the final velocity of the boat? Practice 6D and section review

6.3 Elastic and Inelastic Collisions In a collision, the total momentum (of the system) is conserved. The momentum lost by one object is equal to the momentum gained by another object. There are 3 types of collisions Perfectly Inelastic Inelastic Elastic While total momentum is conserved, the total KE is generally NOT conserved. Energy can converted to internal energy when objects deform or sound etc.

Perfectly Inelastic Collisions Perfectly inelastic collisions are those in which the colliding objects stick together and move with the same velocity. Kinetic energy is generally not conserved. Ex: Meteorite collides head on with Earth and becomes buried in it’s surface m1v1i + m2v2i = (m1 + m2)vf

Sample 6E m1v1i + m2v2i = (m1 + m2)vf A 1850 kg luxury sedan stopped at a traffic light is struck from the rear by a compact car with amass of 975 kg. The two cars become entangled as a result of the collision. If the compact car was moving at a velocity of 22.0 m/s to the north before the collision, what is the velocity of the entangled mass after the collision? m1v1i + m2v2i = (m1 + m2)vf

Inelastic Collisions m1v1i + m2v2i = (m1 + m2)vf Kinetic energy is converted to internal when the objects are deformed during the collision. Some KE is converted to sound energy also Momentum is conserved. m1v1i + m2v2i = (m1 + m2)vf The decrease in KE an be found using the formula ∆KE= KEf-KEi

Sample 6F Two Clay balls collide head-on in a perfectly inelastic collision. The first balkl has amass of 0.500 kg and an initital velocity of 4.0 m/s to the right. The mass of the second ball is 0.250 kg, and it has an initial velocity of 3 m/s to the left. What is the final velocity of the composite ball of clar after the collision? What is the decrease in KE during the collision? m1v1i + m2v2i = (m1 + m2)vf ∆KE= KEf-KEi

Elastic Collisions Momentum and kinetic energy are conserved in an elastic collision. Two objects collide and return to their original shapes with NO loss of kinetic energy. BOTH momentum and KE are conserved. Elastic refers to something that returns to or keeps its shape m1v1i + m2v2i = m1v1f + m2v2f

Sample 6G Use problem 1 in practice 6G

Directions for Velocity Momentum is a vector, so direction is important. (N, E + S,W-) Velocities are positive or negative to indicate direction. Example: bounce a ball off a wall

Elastic Inelastic Sticky Bouncy Ke is Not conserved Ke is conserved Bullet in wood car bumper v>5mph irreversible Bouncy Ke is conserved spring bumper Molecules reversible Practice 6G & Section Review

Recoil Recoil is the term that describes the backward movement of an object that has propelled another object forward. In the nuclear decay example, the vn’ would be the recoil velocity.