Untitled Notes

In this lesson, we:
- Learn that an object’s momentum is the “amount of motion” it has due to its mass and velocity.
- Show that momentum during collisions and explosions is conserved by transfer of momentum between objects.
- Find out whether collisions are elastic or not by calculation.
- Use conservation of momentum concepts to solve exam-type problems.

When analyzing a situation, focus on specific objects referred to as the system.
Common examples utilize two or three objects interacting through collisions or explosions.
A method for describing the motion of these objects before and after interactions is necessary.

The momentum of an object is described as the amount of motion it possesses, which is calculated as follows: $ext{Momentum} = ext{mass} imes ext{velocity}$
- The unit of momentum is $ext{kg} imes ext{m/s}$ .
- Momentum is a vector quantity, meaning that direction is significant for determining an object's momentum.

When objects with momentum touch:
- They exert forces on each other.
- According to Newton’s third law, the force exerted between them is equal in magnitude but opposite in direction.
- The contact time during which they exert these forces is the same for both objects.
- Consequently, this results in equal but opposite changes in their momenta, thus conserving the total momentum in the system.
Impulse is defined as the change in motion experienced by an object due to a force acting over a specified time period.
- Important Note: The force utilized in impulse calculations is also a vector, allowing it to carry a positive or negative sign to indicate its direction.

As previously stated, impulse represents how objects exchange momentum, maintaining the system's total momentum constant.
Important considerations when dealing with conservation of momentum questions include:
- The total momentum of all objects in the system before a collision is to be determined.
- The total momentum after the collision must also be calculated.
- Equate the two total momentum values and solve for any unknowns.
Steps to approach these questions:
1. Diagram and Direction:
  - Draw a quick sketch indicating the direction labeled as positive.
  - Stick to the chosen direction throughout the calculations.
  - Make sure to represent the objects in the system before and after the interaction.
2. Conservation Equation:
  - Set up the conservation of momentum equation based on the number of objects involved.
  - Each object contributes its individual momentum to the equation.
  - Example with two objects colliding and separating: The equation has four terms (two before, two after).
  - Example with two objects colliding and combining: The equation has three terms (two before, one after).
  - Example with one object exploding: The equation has three terms (one before, two after).

While momentum is conserved during a collision, the conservation of kinetic energy must also be examined.
If kinetic energy post-collision equals the pre-collision amount, it is classified as an elastic collision.
Conversely, if kinetic energy is lost, the collision is termed inelastic.
Often, proving this involves calculations for kinetic energy before and after the collision.

Context: Two shopping trolleys, X and Y, are moving right along a straight line.
Specifications:
- Mass of trolley Y: 12 kg
- Kinetic energy of trolley Y: 37.5 J
1. Calculate the speed of trolley Y:
- Use the equation: ext{K.E.} = rac{1}{2} m v^2,
- Rearranging gives: v = ext{sqrt}igg(rac{2 imes ext{K.E.}}{m}igg).
1. Momentum Question:
- Trolley X (mass 30 kg) collides with trolley Y, and they stick together upon impact.
- Post-collision combined speed of the trolleys: 3.2 m/s.
  - Calculate the speed of trolley X before the collision using conservation of momentum.
1. Collision Dynamics:
- Trolley X exerting a force on trolley Y during the collision (duration: 0.2 s).
- The relevant equation here would involve impulse:
  $F imes t = ext{change in momentum}$ .

System: The collection of objects concerned in the analysis.
Momentum: The quantity of motion a body holds due to its mass and velocity.
Conservation of Momentum: The principle that the total linear momentum of a closed system remains unchanged or constant.
Impulse: The change in momentum of an object due to a force applied over a period of time.
Collision: The rapid interaction occurring when two or more objects strike one another.
Explosion: A sudden and forceful separation of objects.
Elastic collision: A collision in which kinetic energy is conserved.
Inelastic collision: A scenario where kinetic energy is not conserved and some amount is lost.

Consider two rugby players running towards each other.
- A smaller and lighter player must run faster to effectively stop the larger player running in the opposite direction.
Momentum before and after the collision amounts to zero, as their directions are opposite:
$ext{momentum}_{before} = p_1 + (-p_2) = 0$ .
Even if they stop each other entirely, the total momentum remains zero, verifying that momentum is conserved.

Question 1: (DOE March 2010 Question 3.2) A net force F acts on two isolated objects, P and Q. The mass of Q is three times that of P. Ignore friction. If the rate of change of momentum of object Q is x, what is the rate of change of momentum of object P?
- A) x
- B) x
- C) x
- D) 3x
Question 2: (DOE March 2010 Question 4) A police officer fires a bullet (mass 15 g) into a stationary wooden block (mass 5 kg), which is suspended. The bullet remains embedded in the block, swinging to a height of 15 cm post-impact.
a) State the law of conservation of momentum in words.
b) Use energy principles to demonstrate that the initial velocity of the block-bullet assembly is 1.71 m/s immediately after impact.
c) Calculate the bullet's velocity just before impact.
d) Explain why the police officer is pushed back when firing his rifle using relevant laws of motion.

Learn Xtra LIVE SHOW NOTES: GRADE 12 PHYSICAL SCIENCES
Links:
- http://www.mindset.co.za/learn/xtra
- http://www.education.gov.za/Examinations/PastExam Papers/tabid/351/Default.aspx
- http://phet.colorado.edu/en/simulation/collision-lab
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