Momentum and Its Conservation Chapter 9 Momentum and Its Conservation

Momentum is the product of an object’s mass and velocity. Formula for momentum Momentum is the product of an object’s mass and velocity. p=mv

Why p? Momentum is so fundamental in Newtonian mechanics that Newton called it a “quantity of motion” Mathematician Gottfried Leibniz used the term progress to mean “quantity of motion with which a body proceeds in a certain direction”.

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.

Basic Momentum Problems Directions: Solve for the momentum problems below. Make sure to put these in your NOTEBOOK! A. 75 kg speed skater moving forward at 16 m/s B. 135 kg ostrich running north at 16.2 m/s C. 5.0 kg baby on a train moving eastward at 72 m/s D. 0.8 kg kitten running to the left at 6.5 m/s E. 48.5 kg passenger on a train stopped on the tracks

Law of Conservation of Momentum Total Initial Momentum = Total Final Momentum

COLLISIONS

Types of Collisions Elastic vs. Inelastic Elastic Collision- Two objects collide and move separately after the collision. The total momentum and the total kinetic energy is conserved

Inelastic Collision A collision in which two objects stick together after colliding. Momentum is conserved The final velocity is the same for both objects since they are stuck together

You need to be able to: Apply conservation of momentum to solve simple collision problems. (P3.5a)

What type of collision?

Find the velocity of the ice skater Law of Conservation of energy states that momentum before collision=momentum after the collision Before p=(12 kg)(20 km/h)=240 After p= (75kg)v V=3.2 km/h

Which type of collision? What is the final velocity?

Which type of collision? What is the final velocity?

Assignment: PAPER WAD 1. Write a momentum collision story problem similar to the examples given in class on a lined piece of paper. DO NOT SOLVE. 2. Crumple up paper wad. Throw it to classmate! 3. Solve the problem. 4. Crumple up paper wad. Throw it to classmate! 5. Check answer. Write a momentum story problem. 6. Crumple up paper wad. Throw it to classmate! 7. Solve the problem. 8. Crumple up paper wad. Throw it to classmate! 9. Check answer……

Impulse and Momentum 9.1 Impulse and Momentum Section Impulse and Momentum 9.1 Impulse and Momentum Impulse- the product of the average force on an object and the time interval over which it acts. Impulse= FΔt Units are N*s

Impulse and Momentum 9.1 Impulse and Momentum Section Impulse and Momentum 9.1 Impulse and Momentum Recall the equation (2nd Law) F=ma, then F=m(Δv/t). It can be rearranged so that FΔt = mΔv The right side of this equation, pf − pi, describes the change in momentum of an object. Thus, the impulse on an object is equal to the change in its momentum, which is called the impulse-momentum theorem. FΔt = pf − pi

Impulse and Momentum 9.1 Using the Impulse-Momentum Theorem Section Impulse and Momentum 9.1 Using the Impulse-Momentum Theorem Impulse is the area under a curve on force-time graphs. In this graph the impulse =13.1 N·s Because 1 N·s is equal to 1 kg·m/s, the momentum gained by the ball is 13.1 kg·m/s in the direction of the force acting on it.

Section Impulse and Momentum 9.1 Using the Impulse-Momentum Theorem to Save Lives Air bags- exert force on larger area of a person’s body, reducing the force during collision. Also, air bags increase the time interval . The cushions in athletic shoes are designed to reduce the force of impact by increasing the time interval of when the force is applied to the ground.

Conservation of Momentum Section Conservation of Momentum 9.2 Momentum is conserved in a Closed, Isolated System Under these conditions, the law of conservation of momentum states that the momentum of any closed, isolated system does not change The first and most obvious condition is that no balls are lost and no balls are gained. Such a system, which does not gain or lose mass, is said to be a closed system. When the net external force on a closed system is zero, the system is described as an isolated system.