Foundations of Physics

1. Foundations of Physics Workshop: The Momentum Collider

2. The Momentum Collider CPO Science

3. Key Questions • What is Momentum? • What are some useful properties of momentum? • How can we measure and observe momentum? • What role does momentum play in collisions and how can we use it for calculations?

4. What is Momentum? • Property of moving matter • Like mass, it measures an object’s resistance to a change in speed or direction • The product of an object’s mass and velocity • IMPORTANT – Remember velocity is a vector so DIRECTION is very important

5. Setting up the Collider • Allows us to measure and observe momentum • The collider is level and plumb • This ensures the projectile and target will collide squarely • Practice releasing the projectile a few times

6. Two Objects • Loop the String of the Target over the post on the side of the hanger • Take a few practice swings with the projectile to get a feel for the release

7. Measure the Projectile’s Velocity • Loop the String of the Target over the post on the side of the hanger • Only the projectile will be swung • Swing the projectile through the photogates once, then catch it so it does not swing back through • Calculate the velocity of the projectile; the diameter of the projectile is 2.50 cm • Velocity is a vector!! It is direction sensitive!

8. Collect Data • Use the CPO Data Collector and photogates to see how long it takes the marble to break the light beam at points A and B • Calculate speeds

9. Investigate Motion of Projectile • How would you calculate the velocity?

10. What about MASS? • Don’t we need MASS to calculate momentum? • We will calculate the mass of the target from our measurements of velocities and the mass of the projectile at the end • How? We will use a “conservative” approach

11. Conservation of Momentum • Like energy, momentum obeys a conservation law • After the collision both balls may be moving with different speeds and in different directions • the total momentum after the collision must be equal to the total momentum before the collision • mpv0 = mtvt + mpvp

12. Different Kinds of Collisions • In an elasticcollision, the objects bounce off of each other with no loss in the total kinetic energy. • In an inelasticcollision, objects may change shape, stick together, or ‘lose’ some kinetic energy to heat, sound, or friction. • Momentum is conserved in both elastic and inelastic collisions, even when kinetic energy is not conserved.

13. Two Objects…Again • This time we will use both objects to perform a collision (target diam. 3.175 cm) • Double check to make sure they are aligned • Predict with your group – Elastic or Inelastic?

14. Performing A Collision • Allows us to measure and observe momentum • The collider is level and plumb • This ensures the projectile and target will collide squarely

15. Observations • The projectile collided with the target • The projectile actually bounced backward in the opposite direction! • The target swung in the same direction as the projectile, even though the projectile “bounced off” it • Try it again but this time, record data

16. Calculate the Three Velocities • 1st velocity– the velocity of the projectile as it approaches the collision vo • 2nd velocity– the velocity of the projectile as it bounces back vp • 3rd velocity– the velocity of the target after the collision vt

17. Using Conservation of Momentum • the total momentum after the collision must be equal to the total momentum before the collision. Insert velocity values in cm/sec • mpv0 = mtvt + mpvp

18. Conservation of Momentum • mp113.9= mt74.5 + mp-32.3 • mp113.9= mt74.5 - mp32.3 • Don’t Forget About Direction! • mp146.2= mt74.5

19. mp146.2= mt74.5 • Divide both sides by 74.5 • mp146.2/74.5= mt • mp1.96= mt • If the projectile ball has a mass of 67.2 g, what is the mass of the target ball?

20. We have used Momentum • We calculated the ratio of the masses involved in the collision • We used the Conservation of Momentum Equation to do it • What would happen if they were the same mass? • What are other ways you can think of to use this equation?