Study Guide on Momentum and Impulse

Following the declaration of COVID-19 as a global pandemic, teaching and learning in South Africa faced significant disruptions. Many students had reduced classroom time due to phased in and rotational attendance. Schools could not complete all the content as outlined in the Curriculum and Assessment Policy Statements (CAPS).
To mitigate these issues for the current Grade 12 students, the Department of Basic Education (DBE) collaborated with subject specialists from Provincial Education Departments (PEDs) to create a Self-Study Guide, covering essential topics, skills, and concepts critical for Grade 12.
The aim is to address pre-existing content gaps and foster independent learning and mastery of core concepts.

This guide focuses on the topic of momentum and impulse.
It should be used alongside the CAPS document and examination guidelines.
Additional resources like textbooks and past exam papers should be utilized to reinforce content.
Students should familiarize themselves with the glossary of terms and ensure they understand all definitions.
Working through examples and exercises is crucial for understanding; compare answers with the memorandums after completing exercises to identify and learn from mistakes.
Accessing the formula sheet provided in this guide is necessary; there is no need to memorize formulas.

Momentum: Defined as the product of an object’s mass and its velocity.
- Formula: $p = mv$
Units: kg·m/s (kilogram meter per second)
Always convert mass to kg and velocity to m/s. Indicate direction using + and - signs. A negative vector indicates the opposite direction.
Momentum is a vector quantity and must be dealt with algebraically considering direction.

A dog with mass 30 kg runs at a velocity of 5 m/s. Calculate its momentum:
- Solution: $p = 30 ext{ kg} imes 5 ext{ m/s} = 150 ext{ kg·m/s (East)}$
A car with mass 250 kg moves at 60 m/s:
- Solution: $p = 250 ext{ kg} imes 60 ext{ m/s} = 15000 ext{ kg·m/s (in the direction of motion)}$

The change in momentum (Δp) can be calculated, indicating the direction based on the selected coordinate system.
Example: A tennis player serves a ball, and if the momentum changes from 10 kg·m/s east to 10 kg·m/s west:
- Change in momentum $ext{Δ}p = p_{final} - p_{initial} = -10 ext{ kg·m/s} - 10 ext{ kg·m/s} = -20 ext{ kg·m/s}$

Law of Conservation of Momentum: In an isolated system, the total momentum before and after an event (like a collision) remains constant.
- Formula: $p_{total, initial} = p_{total, final}$
Illustrated through two possibilities of collisions: elastic where kinetic energy is conserved, and inelastic where it is not.

Elastic Collision: Two snooker balls collide, conserve both total linear momentum and kinetic energy.
Inelastic Collision: Cars collide and stick together, only the total momentum is conserved.
Explosive Scenario: Initially joined objects separate after impact.

A girl of mass 30 kg jumps onto a stationary cradle of mass 2 kg:
- Use $m_1v_1 + m_2v_2 = (m_1 + m_2)v_f$ to solve for final velocity. If $v_f$ is the common velocity after the girl jumps onto the skateboard, the equation simplifies to yield the final velocity.

Impulse: The product of the net force acting on an object and the time interval over which it acts.
- Formula: $I = F imes t$
- Unit of Impulse: kg·m/s but can also be expressed as Newton-seconds.
The relation of impulse to momentum is given by $I = ext{Δ}p$ , demonstrating that impulse is equivalent to the change in momentum.

By increasing the time of contact in collisions (as airbags do), the impulse and thus the force experienced by occupants are reduced.

A formula sheet will be available.
Comfort with this resource is essential, particularly understanding which formulas apply to momentum and impulse.

Ensure to study definitions related to momentum and impulse and understand their derivations to reinforce memory.

Definitions related to momentum, impulse, collisions, contact forces, etc., must be understood thoroughly for examination success.