Challenge_Impulse_Momentum.pptx (3)

Challenge – Impulse & Momentum

Starter Question: How do air bags work?

• Think about impulse and momentum change when considering the safety features in vehicles.

• Describe the process considering: force, impact time, and how these factors contribute to passenger safety during collisions.

Definitions

• Impulse:

  • Definition: Impulse is defined as the product of force and the duration of time over which that force acts. It reflects how a force changes the momentum of an object.

  • Formula: [ J = F × Δt ]

• Momentum:

  • Definition: Momentum is defined as the product of the mass of an object and its velocity. It is a vector quantity, meaning it has both magnitude and direction.

  • Formula: [ p = mv ]

Connection

• Impulse and momentum are intrinsically linked through changes in motion under force. When an object experiences a force over time, its momentum changes, which is precisely what impulse quantifies.

The Impulse-Momentum Theorem

• Foundation:

  • The theorem is grounded in Newton’s 2nd Law of Motion, which states that Force (F) is equal to mass (m) multiplied by acceleration (a).

• Acceleration Revisit:

  • Recall that acceleration can be expressed as the change in velocity (Δv) divided by the change in time (Δt). Thus, [ a = \frac{Δv}{Δt} ]

• Rearranging the Equation:

  • By substituting acceleration, we rearrange to find that: [ F = m \left( \frac{Δv}{Δt} \right) ]

  • Multiplying both sides by time results in: [ F Δt = m Δv ]

• Conclusion:

  • The impulse experienced by a body (J) is equal to its change in momentum (Δp), which can be expressed as: [ J = Δp ]

Example Calculation

• Situation:

  • Consider a 70-kg person driving at 20 m/s who strikes a tree and comes to a stop in 0.10 seconds.

  • Question: What force is experienced by the driver?

• Calculations:

  • Given the formulas: [ J = Δp ][ F Δt = m Δv ][ F = \frac{m Δv}{Δt} ]

  • Substitute in the known values: [ F = \frac{70 \text{ kg} \times 20 \text{ m/s}}{0.1 \text{ s}} ]

  • Result: [ F = 14,000 \text{ N} ]

  • Consideration:

  • Reflect on what other factors, such as the driver's reaction time, the crumple zone of the vehicle, and the potential for secondary impacts, are not accounted for in this calculation.

Air Bags

• Definition and Purpose:

  • Airbags are a crucial component in modern vehicle safety systems designed to minimize risk and injury during collisions by controlling the deceleration of passengers.

• Impact of Air Bags on Calculation:

  • Question: Which quantity do airbags primarily affect in our calculation? Options:

    • A) Δt (impact time)

    • B) m (mass)

    • C) v (velocity)

Extended Air Bag Time Calculation

• Scenario:

  • If an airbag extends the driver’s crash time from 0.10 s to 1.0 s, we need to recalculate the new force experienced by the driver.

• Recalculations:

  • Use the same formulas: [ J = Δp ][ F Δt = m Δv ][ F = \frac{m Δv}{Δt} ]

  • Substitute new impact time: [ F = \frac{70 \text{ kg} \times 20 \text{ m/s}}{1.0 \text{ s}} ]

  • Result: [ F = 1,400 \text{ N} ]

Another Application:

• Encourage deeper exploration into various real-life applications of impulse and momentum—such as sports science, car safety design, and physics of gymnastics—highlighting their significance in everyday scenarios.