Lecture26_Conservation_of_Momentum

Momentum and Force

• Momentum: Vector characteristic of the "quantity of motion."

• Newton's Second Law: Changes in momentum due to impulse of total force: p = F Δt

• Momentum formula: p = mv

Conservation of Momentum

• Total Momentum: Vector sum of momenta in a system.

• Conservation Principle: Total momentum conserved if no external unbalanced forces are present.

• Momentum-Impulse principle: [ P = p_1 + p_2 = 0 ]

  • For systems with external force: [ P + F_{ext} dt = P_f ]

Spring and Two Masses Problem

• Two masses (M and 3M) are pushed apart by a spring.

• Speed relation: Speed of mass M is _____ speed of mass 3M. (Options: A. same, B. twice, C. three times, D. four times.)

Choice of the System

• Momentum Conservation: Depends on system choice.

• If both objects are included, momentum is conserved. If only one object is included, it's not conserved.

Kinetic Energy Relation (Spring)**

• The kinetic energy of mass M is _____ the kinetic energy of mass 3M. (Options: A. same, B. three times, C. nine times, D. one third of, E. one ninth of.)

Throwing a Ball

• Two people throw a ball back and forth on roller blades.

• After a couple of throws, options for their positions: A. same, B. farther apart, C. closer, D. moving away, E. moving towards each other.

Rain Filling a Railroad Car

• As rain accumulates in a moving railroad car, options for speed: A. decreases, B. does not change, C. increases.

• Horizontal momentum of car + rainwater system is conserved.

Asteroid Collision

• Asteroid A (2000 kg) and B (3000 kg) collide and stick: Calculate speed after collision.

• Options for speed: A. 29.0 m/s, B. 32.9 m/s, C. 36.4 m/s, D. 37.0 m/s, E. 50.0 m/s.

Problem Solving Procedure

1. Draw a picture.

2. Identify independent bodies.

3. Identify forces (draw FBDs).

4. Select a system and determine internal/external forces.

5. Choose initial and final points.

6. Write conservation of momentum in vector form.

7. Select coordinate axes.

8. Rewrite conservation of momentum in components.

9. Solve equations analytically.

10. Plug in numbers.