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1. Chapter 9: Momentum and conservation of momentum

2. Momentum The product of the mass and velocity of a body Represented by p in the equation p = mv A change in momentum is represented in the equation ∆p = m∆v Velocity of an object is constant unless a force is acting on the object, this is represented in the equation F = ma = (m ∆v)/∆t
3. Impulse Impulse is the product of the net force and the time interval over which it acts Impulse is represented in the equation F∆t = m∆v Impulse given to an object is equal to the change in momentum of the object This is known as the impulse-momentum theorem The impulse-momentum theorem is represented in the equation F∆t = ∆p
4. Impulse-momentum theorem (IMT) Force is not constant in IMT Use average force when calculating IMT Large impulse = large ∆p Large impulse can also = large force over a short time or small force over a long time
5. Example Problem A baseball of mass 0.14kg is moving at 35m/s. A) find the momentum of the baseball. B) Find the velocity at which a bowling ball, mass 7.26kg, would have the same momentum as the baseball.
6. Example #2 A 0.144kg baseball is pitched horizontally at 38m/s. After it is hit by a bat, it moves horizontally at -38m/s. A) What impulse did the bat deliver to the ball? B) If the bat and ball were in contact 0.0008s, what was the average force the bat exerted on the ball? C) Find the average acceleration of the ball during its contact with the bat.
7. Homework Practice Problems #1-3 pp. 178-179
8. Angular momentum Angular momentum is the momentum of an object travelling in a circle. It is the product of the objects mass, velocity, distance from the center of the circle, and the component of velocity perpendicular to that of distance from the center of the circle
9. Conservation of momentum Based on a closed system A system is a defined collection of objects A closed/isolated system is a defined collection of objects where objects neither leave or enter the system Momentum is constant in a closed system The initial momentum = final momentum in a closed system Impulse and change in momentum always equal zero for a closed system Each object in the system can experience impulse and/or momentum change but the system does not
10. Momentum of a closed system Represented by the sum of the initial momentum of each object in the system equaling the sum of the final momentum of each object in the system pai + pbi = paf + pbf Momentum is always conserved in closed systems, meaning initial momentum will always equal final momentum in a closed system. This is known as the Law of Conservation of Momentum (LCM) We can determine the velocity or mass of an object in the system or even that objects momentum using the LCM
11. Law of Conservation of Momentum (LCM) Using the equation for momentum for each object in the system we can determine an individual objects velocity, mass, or momentum For example: pai + pbi = paf + pbf also can equal: maivai+ mbivbi = mafvaf + mbfvbf We can also determine the change in momentum for individual objects in the system ∆pa =paf - pai We can also say the momentum gained by one object in the system is lost by another, thus momentum is transferred between objects in the system ∆pa = -∆pb
12. Example #3 Glider A of mass 0.355kg moves along a frictionless air track with a velocity of 0.095m/s. It collides with glider B of mass 0.710kg moving in the same direction at a speed of 0.045 m/s. After the collision, glider A continues in the same direction with a velocity of 0.035m/s. What is the velocity of glider B after the collision?
13. Homework Practice problems #5-7 on pp. 185
14. Internal and external forces Internal forces are the forces acting inside a closed system External forces are the forces that act on a system but are not defined in the system If external forces are present the system is no longer a closed system and may need to be redefined
15. Rockets and momentum Rockets are propelled using momentum The rocket is carrying fuel which it burns and then expels the exhaust gasses When the rocket expels the exhaust it pushes the rocket forward as the gasses are expelled backward The rockets velocity increases as it’s mass decreases The gas’s velocity is high and it’s mass is low but it’s momentum is equal to the momentum it transferred to the rocket Be sure when working equations involving rockets that you subtract the mass of the gas from the initial mass of the rocket
16. Example #4 An astronaut at rest in space with a mass of 84kg fires a thruster that expels 0.035kg of hot gas at 875m/s. What is the velocity of the astronaut after firing the shot?
17. Conservation of momentum in 2 directions Momentum is still conserved even if the objects have different directions after the collision than they had before.
18. Example #5 A 2.00kg ball, A, is moving at a velocity of 5.00m/s. It collides with a stationary ball, B, also of mass 2.0kg. After the collision, ball A moves off in a direction 30.0 degrees to the left of its original direction. Ball B moves off in a direction 90.0 degrees to the right of ball A’s final direction. A) draw a vector diagram to find the momentum of ball A and ball B after the collision B) Find the velocities of each ball after the collision.
19. Homework Practice Problem #14 pp. 191