Evaluate Collision Design Solutions - Physics
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What formula defines linear momentum used to compare collision design options?
What formula defines linear momentum used to compare collision design options?
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$p=mv$. Momentum equals mass times velocity.
$p=mv$. Momentum equals mass times velocity.
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What is the difference between a design criterion and a design constraint?
What is the difference between a design criterion and a design constraint?
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Criterion: desired performance; constraint: nonnegotiable limit. Criteria are goals to optimize; constraints are absolute requirements.
Criterion: desired performance; constraint: nonnegotiable limit. Criteria are goals to optimize; constraints are absolute requirements.
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What is the impulse–momentum relation used to compare collision designs?
What is the impulse–momentum relation used to compare collision designs?
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$J=\Delta p=F_{avg}\Delta t$. Impulse equals momentum change and average force times time interval.
$J=\Delta p=F_{avg}\Delta t$. Impulse equals momentum change and average force times time interval.
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What equation links average impact force to stopping time for fixed momentum change?
What equation links average impact force to stopping time for fixed momentum change?
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$F_{avg}=\frac{\Delta p}{\Delta t}$. Rearranging impulse-momentum theorem to isolate average force.
$F_{avg}=\frac{\Delta p}{\Delta t}$. Rearranging impulse-momentum theorem to isolate average force.
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Which design change reduces peak force most directly when $\Delta p$ is fixed: increase or decrease $\Delta t$?
Which design change reduces peak force most directly when $\Delta p$ is fixed: increase or decrease $\Delta t$?
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Increase $\Delta t$. Longer collision time spreads force over more time, reducing peak.
Increase $\Delta t$. Longer collision time spreads force over more time, reducing peak.
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What is the work–energy relation used to evaluate stopping distance designs?
What is the work–energy relation used to evaluate stopping distance designs?
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$W=\Delta K$. Work done equals change in kinetic energy for stopping analysis.
$W=\Delta K$. Work done equals change in kinetic energy for stopping analysis.
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What kinetic energy formula is used when comparing energy absorption in crashes?
What kinetic energy formula is used when comparing energy absorption in crashes?
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$K=\frac{1}{2}mv^2$. Standard kinetic energy formula for calculating crash energies.
$K=\frac{1}{2}mv^2$. Standard kinetic energy formula for calculating crash energies.
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If speed doubles, by what factor does kinetic energy increase in $K=\frac{1}{2}mv^2$?
If speed doubles, by what factor does kinetic energy increase in $K=\frac{1}{2}mv^2$?
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Increases by a factor of $4$. Kinetic energy depends on $v^2$, so doubling $v$ quadruples $K$.
Increases by a factor of $4$. Kinetic energy depends on $v^2$, so doubling $v$ quadruples $K$.
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What is the momentum formula used to compare collision outcomes?
What is the momentum formula used to compare collision outcomes?
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$p=mv$. Linear momentum equals mass times velocity for collision analysis.
$p=mv$. Linear momentum equals mass times velocity for collision analysis.
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What conservation law is typically applied to an isolated collision system?
What conservation law is typically applied to an isolated collision system?
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Total momentum is conserved. No external forces means system momentum stays constant.
Total momentum is conserved. No external forces means system momentum stays constant.
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In an isolated collision, what equation expresses momentum conservation for two objects?
In an isolated collision, what equation expresses momentum conservation for two objects?
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$m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}$. Initial total momentum equals final total momentum.
$m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}$. Initial total momentum equals final total momentum.
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Which collision type maximizes kinetic energy after impact: elastic or perfectly inelastic?
Which collision type maximizes kinetic energy after impact: elastic or perfectly inelastic?
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Elastic collision. Elastic collisions conserve kinetic energy; inelastic ones lose it.
Elastic collision. Elastic collisions conserve kinetic energy; inelastic ones lose it.
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What is the defining velocity condition for a perfectly inelastic collision?
What is the defining velocity condition for a perfectly inelastic collision?
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Objects share a final velocity: $v_{1f}=v_{2f}$. Objects stick together, moving with same final velocity.
Objects share a final velocity: $v_{1f}=v_{2f}$. Objects stick together, moving with same final velocity.
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What coefficient of restitution value corresponds to a perfectly inelastic collision?
What coefficient of restitution value corresponds to a perfectly inelastic collision?
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$e=0$. Zero restitution means no relative separation after impact.
$e=0$. Zero restitution means no relative separation after impact.
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What coefficient of restitution value corresponds to a perfectly elastic collision?
What coefficient of restitution value corresponds to a perfectly elastic collision?
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$e=1$. Unity restitution means perfect bounce with no energy loss.
$e=1$. Unity restitution means perfect bounce with no energy loss.
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Which option is a constraint: “minimize peak force” or “mass must be $\le 2.0,\text{kg}$”?
Which option is a constraint: “minimize peak force” or “mass must be $\le 2.0,\text{kg}$”?
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“Mass must be $\le 2.0,\text{kg}$”. Mass limit is a hard requirement (constraint), not a goal.
“Mass must be $\le 2.0,\text{kg}$”. Mass limit is a hard requirement (constraint), not a goal.
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What decision rule selects the best design when multiple criteria have weights?
What decision rule selects the best design when multiple criteria have weights?
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Choose the highest weighted total score. Sum weighted scores for each design; pick the highest.
Choose the highest weighted total score. Sum weighted scores for each design; pick the highest.
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If a design violates any constraint, how should it be treated in evaluation?
If a design violates any constraint, how should it be treated in evaluation?
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Reject or redesign it; it is not acceptable. Constraint violations disqualify designs immediately.
Reject or redesign it; it is not acceptable. Constraint violations disqualify designs immediately.
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Which metric best indicates occupant safety in a crash: maximize $F_{max}$ or minimize $F_{max}$?
Which metric best indicates occupant safety in a crash: maximize $F_{max}$ or minimize $F_{max}$?
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Minimize $F_{max}$. Lower peak forces reduce injury risk to occupants.
Minimize $F_{max}$. Lower peak forces reduce injury risk to occupants.
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If two designs have the same $\Delta p$, which has lower $F_{avg}$: $\Delta t=0.10,\text{s}$ or $0.20,\text{s}$?
If two designs have the same $\Delta p$, which has lower $F_{avg}$: $\Delta t=0.10,\text{s}$ or $0.20,\text{s}$?
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$\Delta t=0.20,\text{s}$. Doubling time halves average force per $F_{avg}=\frac{\Delta p}{\Delta t}$.
$\Delta t=0.20,\text{s}$. Doubling time halves average force per $F_{avg}=\frac{\Delta p}{\Delta t}$.
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Which evaluation tool best organizes criteria, constraints, and scores across designs?
Which evaluation tool best organizes criteria, constraints, and scores across designs?
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A decision matrix (scoring table). Systematically compares designs against all criteria and constraints.
A decision matrix (scoring table). Systematically compares designs against all criteria and constraints.
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Which option best meets the safety criterion if both designs have the same $\Delta p$: larger or smaller $\Delta t$?
Which option best meets the safety criterion if both designs have the same $\Delta p$: larger or smaller $\Delta t$?
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Larger $\Delta t$. Reduces average force via $F_{avg}=\frac{\Delta p}{\Delta t}$.
Larger $\Delta t$. Reduces average force via $F_{avg}=\frac{\Delta p}{\Delta t}$.
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What physics quantity is conserved in an isolated collision and is used as a key criterion?
What physics quantity is conserved in an isolated collision and is used as a key criterion?
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Total momentum, $p_{total}$, is conserved. In isolated systems, momentum before equals momentum after collision.
Total momentum, $p_{total}$, is conserved. In isolated systems, momentum before equals momentum after collision.
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What formula gives impulse, a common criterion for evaluating collision safety designs?
What formula gives impulse, a common criterion for evaluating collision safety designs?
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$J=F\Delta t=\Delta p$. Impulse equals force times time, which equals change in momentum.
$J=F\Delta t=\Delta p$. Impulse equals force times time, which equals change in momentum.
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What relationship shows why increasing collision time reduces average impact force?
What relationship shows why increasing collision time reduces average impact force?
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$F_{avg}=\frac{\Delta p}{\Delta t}$. Longer collision time reduces force for same momentum change.
$F_{avg}=\frac{\Delta p}{\Delta t}$. Longer collision time reduces force for same momentum change.
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What formula defines kinetic energy, often used to judge energy loss in collisions?
What formula defines kinetic energy, often used to judge energy loss in collisions?
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$K=\frac{1}{2}mv^2$. Kinetic energy equals half mass times velocity squared.
$K=\frac{1}{2}mv^2$. Kinetic energy equals half mass times velocity squared.
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What coefficient indicates a perfectly inelastic collision when evaluating design outcomes?
What coefficient indicates a perfectly inelastic collision when evaluating design outcomes?
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$e=0$. Objects stick together with no relative velocity after impact.
$e=0$. Objects stick together with no relative velocity after impact.
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What coefficient indicates a perfectly elastic collision when evaluating design outcomes?
What coefficient indicates a perfectly elastic collision when evaluating design outcomes?
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$e=1$. Objects bounce apart with no kinetic energy loss.
$e=1$. Objects bounce apart with no kinetic energy loss.
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Which equation defines the coefficient of restitution used to compare bounce performance?
Which equation defines the coefficient of restitution used to compare bounce performance?
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$e=\frac{|v_{2f}-v_{1f}|}{|v_{1i}-v_{2i}|}$. Ratio of relative separation to approach velocities.
$e=\frac{|v_{2f}-v_{1f}|}{|v_{1i}-v_{2i}|}$. Ratio of relative separation to approach velocities.
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What is the momentum conservation equation for a 1D two-object collision?
What is the momentum conservation equation for a 1D two-object collision?
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$m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}$. Total momentum before equals total momentum after.
$m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}$. Total momentum before equals total momentum after.
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