Exam question momentum gr 12
Understanding Conservation of Linear Momentum
Introduction to the Problem
- The discussion begins with an overview of the questions that will be addressed, specifically focusing on a collision scenario involving a minibus taxi and a car.
- A minibus taxi traveling south at 20 m/s collides head-on with a car moving north at 15 m/s, setting the stage for analyzing momentum.
Principle of Conservation of Linear Momentum
- The principle states that the total linear momentum before a collision equals the total linear momentum after the collision. This is expressed mathematically as m_1 v_1i + m_2 v_2i = m_1 v_1f + m_2 v_2f.
- Momentum (defined as mass times velocity, mv) is conserved in both magnitude and direction during collisions; it does not disappear or increase.
- The definition emphasizes that in an isolated system, total linear momentum remains constant, which is crucial for solving collision problems.
Analyzing Collision Details
- The driver claims that the taxi was speeding and overloaded. Given data includes: empty taxi mass (2000 kg), average person mass (70 kg), and maximum occupancy (12 people).
- To determine if there were more than 12 passengers, conservation of momentum will be applied to analyze post-collision conditions.
Setting Up Equations
- Using conservation of momentum formula again: m_1 v_1i + m_2 v_2i = (m_1 + m_2)v_f. After collision, both vehicles move together with a common final velocity.
- It’s noted that since they move together post-collision, their final velocities are equal (v_f), simplifying calculations by reducing unknown variables.
Solving for Masses
- Assigning known values: taxi's initial velocity as positive (+20), car's mass as 1248 kg with negative velocity (-15).
- After calculations yield m_taxi = 3120 text kg, subtracting the empty taxi weight reveals passenger weight totaling 1120 kg.
Conclusion on Passenger Count
- Dividing passenger weight by average person mass indicates how many passengers exceeded legal limits in the taxi. Further calculations would provide insights into potential overloading issues.
Occupancy and Inelastic Collisions
Legal Occupancy Limit
- The maximum legal occupancy is 12 people, but there are 16 present, exceeding the limit by 4 passengers.
- The task involves determining how many passengers exceeded this legal limit, which is confirmed to be four.
Understanding Inelastic Collisions
- To show that a collision is inelastic, one must calculate total kinetic energy before and after the collision.
- If the initial kinetic energy equals the final kinetic energy, it’s elastic; if not, it’s inelastic.
Kinetic Energy Calculations
- Initial calculations involve a taxi with a mass of 312 kg moving at 20 m/s and another vehicle with a mass of 1248 kg moving at -15 m/s (considered as positive due to squaring).
- The total initial kinetic energy calculated is 764,400 joules.
Post-Collision Kinetic Energy
- After the collision, both vehicles move at 10 m/s. The total post-collision kinetic energy calculated is 218,400 joules.
- Since initial and final energies differ significantly, this confirms an inelastic collision.
Safety Features in Modern Cars
- Modern cars include safety features like crumple zones designed to absorb impact during accidents.
- Crumple zones help increase the time over which collisions occur, reducing forces experienced by passengers.
Role of Airbags and Seatbelts
- Airbags and seat belts work together to extend the time taken for momentum change during a crash.
- A person without an airbag experiences rapid deceleration compared to someone with an airbag who decelerates more gradually.
Physics Principles Behind Safety Technologies
- Increasing the time of collision reduces net force experienced by passengers; longer duration leads to lower forces acting on them.
- Delta P (change in momentum), which remains constant during collisions, can be managed through technologies that alter delta t (time).
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