Challenge_Impulse_Momentum.pptx (3)

Challenge – Impulse & Momentum

• Starter Question: How do airbags work?

  • Think in terms of impulse and momentum change.

  • Consider the role of force and impact time in the functioning of airbags.

Definitions

Impulse

• Definition: Impulse (J) is the product of force (F) and the time ( Δt) over which that force is applied.

• Formula:

  • J = F × Δt

Momentum

• Definition: Momentum (p) is the product of mass (m) and velocity (v).

• Formula:

  • p = mv

Connection Between Impulse and Momentum

• Impulse is related to momentum because it represents the change in the momentum of an object in a specific time frame.

The Impulse-Momentum Theorem

• Starting Point: From Newton’s 2nd law:

  • F = ma

  • Recall that acceleration (a) can be defined as the change in velocity over the change in time:

    • a = Δv/Δt

  • Substituting this into F = ma gives:

    • F = m (Δv/Δt)

• Multiply both sides by Δt:

  • F Δt = m Δv

• Implication:

  • J = Δp

  • The impulse experienced by a body is equal to its change in momentum!

Example

• Scenario:

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

• Calculation:

  • Using the impulse-momentum theorem:

    • J = Δp

    • F Δt = m Δv

    • Rearranging gives:

      • F = (m Δv)/Δt

    • Where Δv = initial velocity - final velocity (20 m/s - 0 m/s)

  • Substituting Values:

  • F = (70 kg × 20 m/s) ÷ (0.1 s)

  • F = 14,000 N

• Question to Consider:

  • What factors have not been taken into account in this scenario?

Air Bags!

• Airbags are safety devices designed to reduce the forces experienced by vehicle occupants during a collision.

Impact of Air Bags on Quantities Calculated

• Which quantity does an airbag change in the calculations?

  • A) Δt

  • B) m

  • C) Δv

Extended Impact Time With Airbags

• Scenario: Suppose an airbag extended the driver’s crash time from 0.10 s to 1.0 s.

• Revised Calculation for Force:

  • J = Δp

  • F Δt = m Δv

  • F = (m Δv)/Δt

  • Substituting values gives:

    • F = (70 kg × 20 m/s) ÷ (1.0 s)

  • F = 1,400 N

• Conclusion:

  • The force experienced by the driver is significantly reduced due to the extended time of impact.

Another Application

• Explore further applications of impulse and momentum principles.