Evaluate Collision Design Solutions - Physics

1. Which evaluation tool best organizes criteria, constraints, and scores across designs?

   A decision matrix (scoring table). Systematically compares designs against all criteria and constraints.

2. Which collision is more elastic based on $e$: Option A $e=0.30$ or Option B $e=0.80$?

   Option B ($e=0.80$). Higher $e$ means more elastic (closer to 1).

3. What decision rule selects the best design when multiple criteria have weights?

   Choose the highest weighted total score. Sum weighted scores for each design; pick the highest.

4. What formula defines linear momentum used to compare collision design options?

   $p=mv$. Momentum equals mass times velocity.

5. What is the work–energy relation used to evaluate stopping distance designs?

   $W=\Delta K$. Work done equals change in kinetic energy for stopping analysis.

6. If two designs have the same $\Delta p$, which has lower $F_{avg}$: $\Delta t=0.10\,\text{s}$ or $0.20\,\text{s}$?

   $\Delta t=0.20\,\text{s}$. Doubling time halves average force per $F_{avg}=\frac{\Delta p}{\Delta t}$.

7. What kinetic energy formula is used when comparing energy absorption in crashes?

   $K=\frac{1}{2}mv^2$. Standard kinetic energy formula for calculating crash energies.

8. If speed doubles, by what factor does kinetic energy increase in $K=\frac{1}{2}mv^2$?

   Increases by a factor of $4$. Kinetic energy depends on $v^2$, so doubling $v$ quadruples $K$.

9. What equation links average impact force to stopping time for fixed momentum change?

   $F_{avg}=\frac{\Delta p}{\Delta t}$. Rearranging impulse-momentum theorem to isolate average force.

10. What coefficient indicates a perfectly inelastic collision when evaluating design outcomes?

    $e=0$. Objects stick together with no relative velocity after impact.

11. What is the momentum formula used to compare collision outcomes?

    $p=mv$. Linear momentum equals mass times velocity for collision analysis.

12. Which collision type maximizes kinetic energy after impact: elastic or perfectly inelastic?

    Elastic collision. Elastic collisions conserve kinetic energy; inelastic ones lose it.

13. What physics quantity is conserved in an isolated collision and is used as a key criterion?

    Total momentum, $p_{total}$, is conserved. In isolated systems, momentum before equals momentum after collision.

14. Identify the better safety design if $\Delta p$ is fixed: Design A $\Delta t=0.20\,s$ or B $\Delta t=0.10\,s$.

    Design A ($\Delta t=0.20\,s$). Twice the time means half the average force.

15. Which design better meets a 'limit peak force' constraint: A $F_{peak}=900\,N$ or B $F_{peak}=1200\,N$ if limit is $1000\,N$?

    Design A (B violates the $1000\,N$ constraint). B exceeds the maximum allowed force.

16. Which design satisfies a mass constraint of $m\le 2.0\,kg$: Design A $1.8\,kg$ or Design B $2.3\,kg$?

    Design A (Design B violates $m\le 2.0\,kg$). B exceeds the maximum allowed mass.

17. What is the impulse–momentum relation used to compare collision designs?

    $J=\Delta p=F_{avg}\Delta t$. Impulse equals momentum change and average force times time interval.

18. What is the defining velocity condition for a perfectly inelastic collision?

    Objects share a final velocity: $v_{1f}=v_{2f}$. Objects stick together, moving with same final velocity.

19. What coefficient indicates a perfectly elastic collision when evaluating design outcomes?

    $e=1$. Objects bounce apart with no kinetic energy loss.

20. Which design better meets 'maximize energy absorption' if $K_i=10\,J$: A $K_f=2\,J$ or B $K_f=7\,J$?

    Design A ($\Delta K=8\,J$ absorbed). More energy absorbed: $10-2=8\,J$ vs $10-7=3\,J$.

21. Which option best meets the safety criterion if both designs have the same $\Delta p$: larger or smaller $\Delta t$?

    Larger $\Delta t$. Reduces average force via $F_{avg}=\frac{\Delta p}{\Delta t}$.

22. In an isolated collision, what equation expresses momentum conservation for two objects?

    $m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}$. Initial total momentum equals final total momentum.

23. Which metric best indicates occupant safety in a crash: maximize $F_{max}$ or minimize $F_{max}$?

    Minimize $F_{max}$. Lower peak forces reduce injury risk to occupants.

24. Which equation defines the coefficient of restitution used to compare bounce performance?

    $e=\frac{|v_{2f}-v_{1f}|}{|v_{1i}-v_{2i}|}$. Ratio of relative separation to approach velocities.

25. Which design yields smaller average force if both have the same impulse $J$: larger or smaller $\Delta t$?

    Larger $\Delta t$ gives smaller $F_{avg}$. From $F_{avg}=\frac{J}{\Delta t}$, larger time gives smaller force.

26. What is the difference between a design criterion and a design constraint?

    Criterion: desired performance; constraint: nonnegotiable limit. Criteria are goals to optimize; constraints are absolute requirements.

27. What formula defines kinetic energy, often used to judge energy loss in collisions?

    $K=\frac{1}{2}mv^2$. Kinetic energy equals half mass times velocity squared.

28. What coefficient of restitution value corresponds to a perfectly elastic collision?

    $e=1$. Unity restitution means perfect bounce with no energy loss.

29. What formula gives impulse, a common criterion for evaluating collision safety designs?

    $J=F\Delta t=\Delta p$. Impulse equals force times time, which equals change in momentum.

30. Which option is a constraint: "minimize peak force" or "mass must be $\le 2.0\,\text{kg}$"?

    "Mass must be $\le 2.0\,\text{kg}$". Mass limit is a hard requirement (constraint), not a goal.

31. What conservation law is typically applied to an isolated collision system?

    Total momentum is conserved. No external forces means system momentum stays constant.

32. What coefficient of restitution value corresponds to a perfectly inelastic collision?

    $e=0$. Zero restitution means no relative separation after impact.

33. Which option better meets a 'minimize rebound' criterion: Design A $e=0.10$ or Design B $e=0.60$?

    Design A ($e=0.10$). Lower $e$ means less bounce-back velocity.

34. What relationship shows why increasing collision time reduces average impact force?

    $F_{avg}=\frac{\Delta p}{\Delta t}$. Longer collision time reduces force for same momentum change.

35. What is the momentum conservation equation for a 1D two-object collision?

    $m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}$. Total momentum before equals total momentum after.

36. Which design change reduces peak force most directly when $\Delta p$ is fixed: increase or decrease $\Delta t$?

    Increase $\Delta t$. Longer collision time spreads force over more time, reducing peak.

37. If a design violates any constraint, how should it be treated in evaluation?

    Reject or redesign it; it is not acceptable. Constraint violations disqualify designs immediately.

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