1 Honors Physics Chapter 9 Momentum and Its Conservation

2 Honors Physics Skip anything angular in this chapter Lecture Q&A

3 Next Generation Science Standards  HS-PS2-2. Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system.  HS-PS2-3. Apply scientific and engineering ideas to design, evaluate, and refine a device that minimizes the force on a macroscopic object during a collision.

4 Newton’s Second Law Impulse: I = F  t Momentum: P = mv  Nothing but Newton’s Second Law  P is a fundamental quantity that is very useful. Impulse-Momentum Theorem

5 Impulse I = F  t I = Area under curve of Force-Time Graph (Even if F is not a constant.)  Same direction as F Unit of Impulse t F Impulse is a vector

6 Momentum  Remember unit of Impulse Momentum is a vector  Same direction as v Unit of momentum

7 Example: Pg233pp1 A compact car, mass 725 kg, is moving at 115 km/h toward the east. Sketch the moving car. a) Find the magnitude and direction of its momentum. Draw an arrow on your sketch showing the momentum. b) A second car, with a mass of 2175 kg, has the same momentum. What is its velocity?

8 Practice: Pg233pp4 The driver accelerates a kg snowmobile, which results in a force being exerted that speeds up the snowmobile from 6.00 m/s to 28.0 m/s over a time interval of 60.0 s. a) What is the snowmobile’s change in momentum? b) What is the impulse on the snowmobile? c) What is the magnitude of the average force that is exerted on the snowmobile?

9 Practice: The brakes exerts a 640 N force on a car weighing N and moving at 20.0 m/s. The car finally stops. a) What is the car’s mass? b) What is its initial momentum? c) What is the final momentum? d) What is the change in the car’s momentum? e) How long does the braking force act on the car to bring it to a halt?

10 Solution

11 Closed, Isolated System Closed: no objects in or out Isolated: net external force on system is zero

12 Conservation of Momentum The total momentum of any closed, isolated system does not change. The momentum of a single object can change, but the total momentum of the closed, isolated system does not change.

13 Special Case: v 1f = v 2f = v f Totally/Completely Inelastic Collision: the two objects stick together after collision. Final momentum equals to Only if two masses stick together.

14 Example: Pg238pp14 A kg hockey puck moving at 24 m/s is caught and held by a 75-kg goalie who is initially at rest. With what speed does the goalie slide on the ice after the catch?

15 Practice: Pg238pp16 A kg bullet moving at 475 m/s strikes a 2.5-kg bag of flour that is on ice, initially at rest. The bullet passes through the bag, and exits it at 275 m/s. The bag was at rest when it was hit. How fast is the bag moving when the bullet exits?

16 Let original direction of 0.50 kg ball = “+” Practice: Pg238pp18 A 0.50-kg ball that is traveling at 6.0 m/s collides head-on with a 1.00-kg ball moving in the opposite direction at a speed of 12.0 m/s. The 0.50-kg ball bounces backward at 14 m/s after the collision. Find the speed of the second ball after the collision.

17 Internal and External Forces Internal Forces: forces between objects within a system. – Both force giver and receiver are objects within the system – Internal forces do not change the total momentum of the system External Forces: forces from objects outside a system – Force giver is an object outside the system – External forces change the total momentum of the system.

18 Conservation of Momentum of a System Total momentum of a system is conserved only when there is no net external forces. Internal forces do not change the total momentum of a system. – Action and reaction forces cancel out each other.

19 Let right be the positive direction. then Example: Pg240pp20 A thread holds a 1.5-kg cart and a 4.5-kg cart together. After the thread is burned, a compressed spring pushes the cars apart, giving the 1.5-kg cart a speed of 27 cm/s to the left. What is the velocity of the 4.5-kg cart? 1.5 kg 4.5 kg

20 Let Carmen = #1, Judi & canoe = #2, also let forward direction = “+” Then m 1 = 80.0kg, v 1f = 4.0 m/s, m 2 = 115 kg,v 1i = v 2i = 0, v 2f = ? “-” indicates backward direction. Practice: Pg240pp21 Carmen and Judi dock a canoe kg Carmen moves forward at 4.0 m/s as she leaves the canoe. At what speed and in what direction do the canoe and Judi move if their combined mass is 115 kg?

21 Relative Velocity What do we mean when we say Velocity of bullet with respect to the gun is 1000 m/s, or Velocity of bullet relative to gun is 1000 m/s? Muzzle velocity

22 Let you = 1, rock = 2, and the direction you throw the rock = “+”, then Example You (of mass 50 kg) can throw a rock (of mass 2.0 kg) with a maximum relative speed of 10 m/s. If you stand on frictionless ice and throw the rock, what is the maximum possible speed the rock can have (with respect to the ground)?