Evaluate Collision Design - Middle School Physical Science

Find $\Delta p$ if a $1.5\,kg$ object changes velocity from $+4.0\,m/s$ to $0\,m/s$ .

$\Delta p = -6.0\,kg\cdot m/s$ . Change is $p_f - p_i = 0 - 6.0 = -6.0\,kg\cdot m/s$ .
What is a design criterion in a collision-related engineering problem?

A required performance goal the design must achieve. Criteria define measurable targets for successful performance.
Identify whether the constraint is met: limit is mass $\leq 0.50\,kg$ and prototype mass is $0.47\,kg$ .

Constraint met. $0.47\,kg < 0.50\,kg$ , so within the limit.
What is the kinetic energy formula used to evaluate energy changes in a crash test?

$KE=\frac{1}{2}mv^2$ . Kinetic energy equals half mass times velocity squared.
Which metric most directly indicates passenger safety in a crash: peak force or total momentum?

Peak force. Lower peak forces reduce injury risk more than total momentum does.
What is the main purpose of a seat belt in a collision design?

Increase stopping time and spread force over stronger body areas. Restrains occupant to vehicle's deceleration rate.
Identify the better design if $\Delta p$ is equal: Design A $\Delta t=0.20\,s$ , Design B $\Delta t=0.05\,s$ .

Design A (larger $\Delta t$ gives smaller average $F$ ). Using $F = \frac{\Delta p}{\Delta t}$ , longer time means smaller force.
Identify the correct comparison: If $m$ and $v$ are the same, which design has larger $KE$ , $v$ or $2v$ ?

$2v$ (since $KE\propto v^2$ ). Kinetic energy quadruples when velocity doubles ( $KE\propto v^2$ ).
What is the correct decision if a prototype meets all criteria but violates one constraint?

It is unacceptable until the violated constraint is satisfied. All constraints must be met for a valid design.
What is the most appropriate conclusion when a design meets all constraints but fails a key criterion?

It is acceptable by constraints but not successful overall. Must meet both criteria and constraints to succeed.
Find $\Delta p$ if momentum changes from $+3$ to $-1\,\text{kg}\cdot\text{m/s}$ .

$-4\,\text{kg}\cdot\text{m/s}$ . $\Delta p = p_f - p_i = (-1) - (+3) = -4\,\text{kg}\cdot\text{m/s}$
What is the impulse-momentum relationship used to evaluate collision designs?

$J = \\Delta p$ . Impulse equals the change in momentum for any collision.
What is the momentum formula used to evaluate collision outcomes?

$p = mv$ . Momentum equals mass times velocity.
What is the criterion most directly related to safety in a collision design?

Minimizing peak force (or acceleration) on occupants. Lower forces reduce injury risk during impact.
What is a design constraint in a collision-related engineering problem?

A limiting condition such as cost, size, mass, or materials. Constraints set boundaries that cannot be exceeded.
Which design meets the constraint "rebound speed $\le 1\,m/s$ " if measured rebound is $0.8\,m/s$ ?

The design meets the constraint. $0.8\,m/s$ is less than the $1\,m/s$ maximum allowed.
Find the impulse if average force is $30\,N$ applied for $0.40\,s$ .

$J = 12\,N\cdot s$ . Using $J = F\Delta t = 30 \times 0.40 = 12\,N\cdot s$ .
Which statement correctly distinguishes elastic vs. inelastic collisions for evaluation?

Elastic: kinetic energy conserved; inelastic: kinetic energy not conserved. Energy conservation distinguishes collision types.
What design feature most directly reduces peak force by increasing collision time?

Crumple zone (energy-absorbing deformation). Crumple zones extend collision time by deforming, reducing peak forces.
What is the momentum formula used to evaluate how a design changes an object's motion?

$p = mv$ . Momentum equals mass times velocity, measuring an object's motion quantity.
Which collision type best matches a design where objects bounce apart after impact?

Elastic collision. Objects separate after elastic collisions with kinetic energy conserved.
What formula gives momentum for evaluating a moving cart or vehicle before impact?

$p = mv$ . Mass times velocity gives the momentum before collision.
Which option is a valid criterion statement for a crash barrier design?

Keep peak force on the cart below a specified limit. Criteria specify measurable performance goals.
What is the definition of a perfectly inelastic collision in design evaluation?

Objects stick together after impact and move as one. Maximum kinetic energy loss occurs when objects combine.
A cart of mass $2\,kg$ slows from $3\,m/s$ to $0\,m/s$ in $0.5\,s$ ; what is $F_{avg}$ ?

$12\,N$ . $\Delta p = 2(3-0) = 6\,kg\cdot m/s$ ; $F_{avg} = 6/0.5 = 12\,N$ .
Which metric best indicates passenger injury risk in a collision: peak force or total momentum?

Peak force. Higher forces correlate with greater injury severity.
Identify the independent variable when testing how bumper thickness affects peak force.

Bumper thickness. The variable being changed to test its effect.
Which quantity is most directly reduced by increasing collision time in a crash?

Average force, since $F_{avg} = \frac{\Delta p}{\Delta t}$ . Longer collision time reduces force for same momentum change.
What does a crumple zone primarily increase in a collision to meet safety constraints?

Stopping time and stopping distance. Crumple zones extend collision duration by increasing deformation distance.
Which type of collision is more likely to reduce rebound: elastic or inelastic?

Inelastic. Inelastic collisions absorb more energy, reducing bounce-back.
What does a criterion describe when evaluating a collision-related design?

A required performance goal to be met. Criteria define what the design must achieve.
What is a constraint in a collision design problem?

A limit the design must obey (materials, size, time, cost). Constraints are restrictions that bound the design solution.
Identify the best choice if the criterion is minimum rebound speed after impact: lower or higher rebound speed?

Lower rebound speed. Lower rebound means less energy returned, meeting safety goals.
Choose the design that best meets the criterion "minimize force" if $\Delta p$ is equal for both tests.

The design with the larger $\Delta t$ . Larger $\Delta t$ gives smaller $F_{avg}$ for same $\Delta p$ .
Which option is the correct unit for impulse when using SI units?

$N\cdot s$ . Newton-seconds measure impulse in SI system.
Find the average force if $\Delta p=8.0\,N\cdot s$ and $\Delta t=0.20\,s$ .

$F = 40\,N$ . Using $F = \frac{\Delta p}{\Delta t} = \frac{8.0}{0.20} = 40\,N$ .
Choose the safer design if $\Delta p$ is the same: Design A $\Delta t=0.10\,s$ or Design B $\Delta t=0.25\,s$ .

Design B. Longer time ( $0.25\,s > 0.10\,s$ ) means lower force for same impulse.
Which design change most directly reduces $F_{avg}$ if $\Delta p$ stays the same?

Increase the collision time $\Delta t$ . Longer collision time reduces force for same momentum change.
Which option best supports an evidence-based evaluation of a collision design against criteria and constraints?

Use measured data and compare to each requirement. Objective evaluation requires comparing actual test data to specifications.
What is the impulse-momentum relationship used to evaluate collision designs?

$J = F\Delta t = \Delta p$ . Impulse equals force times time, which equals momentum change.
Choose the safer design if both stop the same cart: A has $\Delta t=0.10\,s$ , B has $\Delta t=0.25\,s$ .

Design B. B has 2.5× longer collision time, reducing force.
Which option is a valid controlled variable when testing collision designs: drop height or padding thickness?

Drop height (keep it constant to compare designs fairly). Controlled variables must stay constant; padding varies between designs.
Choose the design that better meets a pressure limit if both have $F=100\,N$ and $A_1=0.02\,m^2$ , $A_2=0.05\,m^2$ .

Design 2 (larger area gives lower pressure). $P_1=5000\,Pa$ , $P_2=2000\,Pa$ , so Design 2 has lower pressure.
What equation gives the change in momentum for an object slowing from $v_i$ to $v_f$ ?

$\Delta p=m(v_f-v_i)$ . Change in momentum is mass times velocity difference.
What is the kinetic energy formula commonly compared before and after a collision?

$KE=\frac{1}{2}mv^2$ . Kinetic energy equals half the mass times velocity squared.
What criterion is directly improved when a design increases collision time $\Delta t$ ?

Lower peak/average force on the object. Extending collision time spreads impulse over longer duration.
What equation relates average force to impulse and collision time in a design test?

$F_{avg}=\frac{\Delta p}{\Delta t}$ . Longer collision time reduces average force for same momentum change.
Which design choice best meets the criterion 'minimize rebound' in a collision test?

Use energy-absorbing, inelastic materials (foam, clay). Inelastic materials absorb energy and prevent bouncing.
What does a free-body diagram show that helps evaluate forces during a collision?

All forces acting on an object during the collision. Arrows represent all forces' magnitudes and directions on the object.
Identify the correct conclusion: If a design meets all criteria but violates one constraint, does it pass?

No; violating any constraint means the design fails. Constraints are mandatory; violating any one causes overall failure.
Identify which design meets the criterion "peak force $\le 30\,\text{N}$ ": A $28\,\text{N}$ , B $35\,\text{N}$ .

Design A. $28\,\text{N}<30\,\text{N}$ meets criterion; $35\,\text{N}>30\,\text{N}$ fails.
Find $F_{avg}$ if a test shows $J=12\,\text{N}\cdot\text{s}$ and $\Delta t=0.60\,\text{s}$ .

$F_{avg}=20\,\text{N}$ . Using $F_{avg} = \frac{J}{\Delta t} = \frac{12}{0.60} = 20\,\text{N}$ .
Which statement defines an elastic collision in terms of kinetic energy?

Total kinetic energy is conserved. No kinetic energy is lost to heat or deformation.
Identify whether the design meets the criterion: stopping time $\ge 0.20\,s$ ; test time $=0.15\,s$ .

Does not meet the criterion. $0.15\,s < 0.20\,s$ , so the time is too short to meet the requirement.
What does it mean if a collision design increases stopping distance while stopping the same object?

It reduces average force by increasing stopping time. Same momentum change over longer time requires less force.
Evaluate a constraint: A rule requires width $\leq 10\,\text{cm}$ . If width is $11\,\text{cm}$ , does it meet the constraint?

No, it violates the width constraint. $11\,\text{cm} > 10\,\text{cm}$ limit, so constraint is violated.
What is the kinetic energy formula used to judge how much energy must be managed?

$KE=\frac{1}{2}mv^2$ . Kinetic energy depends on mass and velocity squared.
Identify the best conclusion if a design increases $\Delta t$ but keeps $\Delta p$ constant.

Average force decreases because $F_{avg} = \frac{\Delta p}{\Delta t}$ . Inverse relationship: doubling time halves average force.
Which option is the correct way to compare prototypes fairly in collision tests?

Keep mass, speed, and impact surface the same for all trials. Controls variables to isolate design differences.
Calculate momentum before impact: $m=2.0\,kg$ and $v=3.0\,m/s$ .

$p = 6.0\,kg\cdot m/s$ . Using $p = mv$ : $2.0\,kg \times 3.0\,m/s = 6.0\,kg\cdot m/s$ .
Which design violates the constraint "mass $\le 120\,g$ " if the prototype mass is $135\,g$ ?

The design violates the constraint. $135\,g$ exceeds the $120\,g$ maximum allowed.
Which design feature most directly increases collision time to reduce injury risk?

Crumple zone (or other energy-absorbing deformation). Deformation extends collision time, reducing peak forces.
Identify whether momentum is conserved for a two-cart system during a brief collision with negligible external forces.

Total momentum is conserved. No external forces means system momentum stays constant.
Identify the best metric to judge "least damage" when comparing two collision designs.

Smallest peak force (or smallest acceleration) on the payload. Lower peak force means less damage to protected object.
What is the correct ranking rule when two designs meet all constraints but differ in criteria?

Choose the design that best meets the prioritized criteria. When constraints are met, criteria performance determines best choice.
What is the correct conclusion if a prototype meets criteria but violates any constraint?

It is unacceptable because constraints are nonnegotiable limits. Constraints are absolute requirements that must be satisfied.
Which comparison best evaluates two designs fairly: same mass and speed, or different mass and speed?

Same mass and speed (controlled variables). Fair tests require identical test conditions except the design feature.
What is a design criterion in a collision-related engineering problem?

A required performance goal the design must achieve. Criteria define what the design must accomplish successfully.
Which design better meets a criterion of minimizing peak force if $J$ is the same but $\triangle t$ is larger?

The design with larger $\triangle t$ . From $F_{avg}=\frac{J}{\triangle t}$ , larger $\triangle t$ gives smaller force.
What is the momentum formula used when evaluating collisions?

$p = mv$ . Momentum equals mass times velocity.
What is the momentum formula used to compare before-and-after collision motion?

Momentum $p = mv$ . Momentum equals mass times velocity.
What design feature increases stopping distance to reduce force during a collision?

Crumple zone or compressible padding. Deformation extends collision time to reduce force.
What does a criterion mean when evaluating a collision-related engineering design?

A desired performance requirement to meet. Criteria are goals the design should achieve for success.
Which measurement is most direct for judging if a design met a 'limit maximum force' constraint?

Measured peak force during impact. Direct force measurement shows if the constraint was met.
What is a design criterion in a collision-related engineering problem?

A required performance goal used to judge success. Criteria define measurable targets for design success.
What is a criterion in an engineering collision-design evaluation?

A required performance goal the design should meet. Criteria are specific goals the design must achieve to be successful.
What does a constraint mean when evaluating a collision-related engineering design?

A limiting condition that must not be violated. Constraints are boundaries the design must stay within.
Calculate $F_{avg}$ if $\Delta p=10\,N\cdot s$ and $\Delta t=0.20\,s$ for a design.

$50\,N$ . $F_{avg} = \frac{10}{0.20} = 50\,N$
Which equation gives average force during a collision from impulse data?

$F_{avg} = \frac{\Delta p}{\Delta t}$ . Rearranged impulse-momentum theorem solving for force.
Which option is the best evidence that a collision design met a force-limit criterion?

Measured peak force is below the specified maximum. Direct measurement confirms the design stays within the force limit.
Calculate $\Delta p$ for $m=0.5\,kg$ , $v_i=4\,m\,s^{-1}$ , $v_f=0$ in a crash test.

$-2\,kg\cdot m\,s^{-1}$ . $\Delta p = 0.5(0-4) = -2\,kg\cdot m\,s^{-1}$
What does it mean if a prototype meets all criteria but violates one constraint?

It is not acceptable; constraints must also be satisfied. Both criteria and constraints must be met for success.
Choose the correct conclusion if results vary widely across trials for the same design.

Reliability is low; more trials or better control is needed. High variability indicates poor experimental control or repeatability.
What relationship explains why increasing collision time can reduce peak force?

$F_{avg}=\frac{\triangle p}{\triangle t}$ . Longer collision time reduces average force for same momentum change.
What is the impulse-momentum relationship used in collision evaluation?

$J = \Delta p = F_{avg}\Delta t$ . Impulse equals change in momentum or average force times time.
Which collision type best matches a design where objects stick together after impact?

Perfectly inelastic collision. Objects that stick have maximum energy loss and no rebound.
Which test result best supports the claim that a bumper design is safer?

It produces a smaller peak force at the same impact speed. Lower peak force means less potential for damage.
What is the definition of an elastic collision used in evaluating designs?

A collision in which kinetic energy is conserved. Total kinetic energy before equals total kinetic energy after.
What equation links impulse and change in momentum for a collision test?

$J = \Delta p$ . Impulse-momentum theorem: impulse equals change in momentum.
Which prototype best meets the criterion if peak force must be $\leq 40\,N$ and results are $38\,N$ , $41\,N$ , and $35\,N$ ?

The $35\,N$ prototype. Only $35\,N$ is below the $40\,N$ limit.
What is a constraint in an engineering collision-design evaluation?

A limit on materials, size, mass, time, or cost. Constraints restrict what resources or parameters can be used in the design.
What is the main purpose of a crumple zone in a collision design?

Increase stopping time and absorb energy to lower peak force. Deformation extends collision time, reducing peak forces.
What is the key safety goal of crumple zones in collision-related design?

Increase collision time to lower force on occupants. Extending collision duration reduces impact forces on passengers.
Which graph would you use to estimate impulse from experimental collision data?

A force–time graph; impulse is the area under the curve. Area under F-t curve equals impulse $J = \int F\,dt$ .
Which option best describes why crumple zones help in collisions?

They increase stopping time, reducing average force. Extending collision time via deformation reduces force.
What does a larger contact area usually do to pressure during a collision?

It reduces pressure for the same force. Pressure equals force divided by area, so larger area means less pressure.
What is the average force during a collision in terms of impulse and time?

$F_{avg} = \frac{\Delta p}{\Delta t}$ . Derived from $J = F_{avg}\Delta t = \Delta p$ .
Which design feature primarily increases $\\Delta t$ in a crash: crumple zone or rigid steel plate?

Crumple zone. Crumple zones deform slowly, extending collision time.
Identify the best decision rule for meeting a criterion: minimize peak force on the passenger.

Choose the design with the smallest measured $F_{max}$ . Lower peak force better protects passengers from injury.
If $\Delta p$ is fixed, what happens to $F_{avg}$ when $\Delta t$ doubles?

$F_{avg}$ becomes half as large. From $F_{avg} = \frac{\Delta p}{\Delta t}$ , doubling denominator halves result.
Identify the dependent variable when testing how bumper thickness affects peak force.

Measured peak force during the collision. The variable being measured as the outcome.
What formula relates impulse to average force and collision time in a design test?

$J = F_{avg}\\Delta t$ . Average force times collision duration gives total impulse.
What is the criterion in a collision design problem?

A desired performance goal the design must achieve. Criteria define what the design should accomplish successfully.
What is a design constraint in a collision-related engineering problem?

A limiting condition such as cost, size, mass, or materials. Constraints are boundaries that restrict design choices.
Identify the best conclusion if a design meets all criteria but violates a cost constraint.

The design is not acceptable because it violates constraints. Violating any constraint makes the design unacceptable.
Which option is the best evidence-based way to rank collision designs against criteria?

Use measured data in a criteria/constraint scoring table. Quantitative comparison ensures objective evaluation.
Select the design that best meets "minimize rebound speed": A rebounds at $1.2\,\text{m/s}$ , B at $0.3\,\text{m/s}$ .

Design B. Lower rebound speed ( $0.3<1.2$ ) better meets minimization goal.
Identify the best evidence that a collision design meets a force-limit criterion.

Measured peak force is at or below the specified limit. Direct measurement confirms criterion compliance.
Which design change increases collision time $\Delta t$ to reduce average force?

Add crumple/foam padding to increase stopping time. Longer collision time reduces force for same momentum change.
Which change best reduces average force in a collision design if momentum change is fixed?

Increase the collision time, $\\Delta t$ . Since $J = F_{avg}\Delta t$ , larger $\Delta t$ means smaller $F_{avg}$ .
Identify the best metric to compare safety between two designs with the same test mass and speed.

Lower peak force (or lower $F_{avg}$ ) on impact. Lower force means less damage or injury potential.
Find $F_{avg}$ if $\Delta p = 4\,\text{N}\cdot\text{s}$ and $\Delta t = 0.20\,\text{s}$ .

$20\,\text{N}$ . $F_{avg} = \frac{\Delta p}{\Delta t} = \frac{4}{0.20} = 20\,\text{N}$
What does impulse represent in evaluating a collision design?

Impulse equals change in momentum: $J=\triangle p$ . Total momentum transfer during collision, regardless of time.
Which graph feature most directly shows a lower peak collision force?

A lower maximum value on the force-versus-time curve. Peak force appears as the highest point on force-time graph.
Identify whether this meets the constraint "mass $\leq 200\,g$ ": prototype mass is $215\,g$ .

No, it violates the mass constraint. $215\,g > 200\,g$ exceeds the mass limit.
What is a constraint in an engineering collision design evaluation?

A required limit such as mass, size, time, or cost. Constraints set boundaries that designs must work within.
Two designs have equal mass and speed; which design has smaller $F_{avg}$ : $\Delta t=0.20\,s$ or $0.40\,s$ ?

The design with $\Delta t = 0.40\,s$ . Longer time gives smaller force when $\Delta p$ is constant.
Identify the correct conclusion if repeated trials give very different peak forces for one design.

The design performance is unreliable due to high variability. Inconsistent results indicate unpredictable performance.
What does a constraint describe when evaluating a collision-related design?

A limit such as cost, mass, size, or materials. Constraints restrict design options and resources.
Which quantity is most directly reduced by adding padding or crumple zones to a design?

Average impact force, $F$ . Padding extends collision time, directly reducing average force.
Identify the safer design: For the same $\Delta p$ , which is safer, $\Delta t=0.10\,\text{s}$ or $\Delta t=0.40\,\text{s}$ ?

$\Delta t=0.40\,\text{s}$ . Longer time ( $0.40\,\text{s}$ ) means lower force, thus safer.
Which option best indicates a design meets a "no damage to cargo" criterion?

Cargo acceleration stays below the specified limit. Staying below damage threshold protects cargo integrity.
Which option is the correct unit for momentum when using SI units?

$kg\cdot m\,s^{-1}$ . SI momentum units combine mass and velocity units.
Identify which design best satisfies a mass constraint: limit $\le 50\,g$ ; Design A $45\,g$ , Design B $55\,g$ .

Design A. $45\,g < 50\,g$ meets the constraint; $55\,g > 50\,g$ exceeds it.
Choose the design that best meets "limit peak force to $\le 15\,\text{N}$ ": A= $12\,\text{N}$ , B= $18\,\text{N}$ .

Design A. Design A's $12\,\text{N}$ is below the $15\,\text{N}$ limit.
What equation defines momentum for comparing pre- and post-collision motion?

$p=mv$ . Momentum is the product of mass and velocity.
Identify whether the design meets the constraint "mass $\le 200\,\text{g}$ " if the prototype mass is $215\,\text{g}$ .

No, it violates the mass constraint. $215\,\text{g} > 200\,\text{g}$ , exceeding the mass limit.
Identify the best metric to compare two designs for occupant safety using sensors.

Lower peak acceleration (or lower peak force) reading. Peak values determine maximum stress on occupants.
What is the kinetic energy formula often used to compare crash severity?

$KE = \frac{1}{2}mv^2$ . Energy of motion depends on mass and velocity squared.
Which metric directly indicates how well a design reduces crash force on an object?

Lower peak force on the object during the collision. Peak force is the maximum force experienced, directly measuring impact severity.
Which design better meets the criterion "reduce average force" if both have same $\Delta p$ but Design A has larger $\Delta t$ ?

Design A. Since $F_{avg} = \frac{\Delta p}{\Delta t}$ , larger $\Delta t$ means smaller force.
Which type of collision best represents a car crash where objects stick together after impact?

Perfectly inelastic collision. Objects combine into one mass moving together after impact.
Find the momentum of a $2.0\,kg$ cart moving at $3.0\,m/s$ .

$p = 6.0\,kg\cdot m/s$ . Using $p = mv = 2.0 \times 3.0 = 6.0\,kg\cdot m/s$ .
Identify whether the design meets the criterion: max force $\le 800\,N$ ; test peak force $=750\,N$ .

Meets the criterion. $750\,N < 800\,N$ , so the force stays below the maximum allowed.
Identify the collision type that best reduces rebound and usually helps lower injury risk.

Inelastic collision. Objects stick together or deform permanently, minimizing dangerous rebounds.
Calculate $p$ for $m=2\,kg$ and $v=3\,m\,s^{-1}$ to compare design test runs.

$6\,kg\cdot m\,s^{-1}$ . $p = mv = 2 \times 3 = 6\,kg\cdot m\,s^{-1}$
What does conservation of momentum mean for an isolated collision system?

Total momentum before equals total momentum after. In isolated systems, momentum is conserved during collisions.
What is a design constraint in a collision-related engineering problem?

A limitation on the design such as cost, size, or materials. Constraints restrict what resources or parameters can be used.
What do the design criteria specify when evaluating a collision-related safety design?

The desired performance goals the design must achieve. Criteria define measurable targets like force reduction or energy absorption.
Which option is the correct constraint statement: "Use only 10 straws and 30 cm tape" or "Prevent damage"?

"Use only 10 straws and 30 cm tape" is the constraint. Material limits are constraints; outcomes are criteria.
Which option is the best metric for comparing two safety designs: lower $F$ or higher $F$ ?

Lower $F$ . Smaller forces cause less damage and improve safety.
What formula gives kinetic energy to compare crash severity at different speeds?

$KE = \frac{1}{2}mv^2$ . Kinetic energy increases with the square of velocity.
What is the definition of an inelastic collision used in evaluating designs?

A collision in which kinetic energy is not conserved. Some kinetic energy converts to heat, sound, or deformation.
Which option is the best decision rule when two designs meet all constraints equally?

Choose the design that best meets the criteria (highest performance). When constraints are equal, optimize for criteria.
Which quantity is most directly reduced by increasing collision time in a crash design?

Average force on the object. Impulse-momentum theorem: longer time means smaller force for same momentum change.
What is the correct statement of conservation of momentum for an isolated two-object collision?

$p_{total,\\,before}=p_{total,\\,after}$ . Total momentum is conserved in isolated collisions.
State the pressure relationship used to evaluate padding or crumple features.

$P=\frac{F}{A}$ . Pressure equals force divided by contact area.
Which prototype meets the mass constraint $m\leq 50\,g$ : A $48\,g$ or B $55\,g$ ?

Prototype A. Only A satisfies the constraint since $48\,g < 50\,g$ .
What is the impulse-momentum relationship used to evaluate collision designs?

$J=\Delta p$ . Impulse equals the change in momentum during collision.
Which collision type has the smallest rebound and most kinetic energy lost: elastic or inelastic?

Perfectly inelastic collision. Objects stick together, converting maximum kinetic energy to other forms.
Identify the metric that best indicates passenger injury risk in a collision test: peak force or mass?

Peak force. Higher forces cause more damage to passengers than mass alone.
What is the impulse formula used to evaluate collision designs?

$J = F\Delta t$ . Impulse equals force multiplied by time duration.
Identify the best evidence that a collision design reduced force: same $\\Delta p$ but larger $\\Delta t$ .

Smaller $F_{avg}$ . From $J = F_{avg}\Delta t$ , if $J$ is fixed and $\Delta t$ increases, $F_{avg}$ decreases.
What key change reduces peak force in a collision design when momentum change is fixed?

Increase the collision time, $\Delta t$ . Longer collision time spreads the same impulse, reducing peak force.
What is the kinetic energy formula used to compare how much energy a design must absorb?

$KE = \frac{1}{2}mv^2$ . Kinetic energy equals half the mass times velocity squared.
Find $p$ for a $0.50\,\text{kg}$ cart moving at $2.0\,\text{m/s}$ .

$1.0\,\text{kg}\cdot\text{m/s}$ . $p = (0.50)(2.0) = 1.0\,\text{kg}\cdot\text{m/s}$
A design criterion says "keep total mass $\leq 250\,g$ "; a prototype is $260\,g$ ; does it meet the constraint?

No, it violates the mass constraint. 260g exceeds the 250g limit.
What do the design constraints specify when evaluating a collision-related safety design?

The limits the design must stay within (materials, cost, size, time). Constraints are boundaries that cannot be exceeded during design.
What does conservation of momentum state for an isolated collision system?

Total momentum before equals total momentum after. No external forces means momentum is conserved.
What is a measurable test metric for the criterion "protect the egg passenger" in a model crash?

Egg remains uncracked after the collision test. Pass/fail metric directly tests protection criterion.
Find $J$ if a cart changes momentum from $2$ to $-4\,\text{kg}\cdot\text{m/s}$ .

$J=-6\,\text{N}\cdot\text{s}$ . Impulse equals final momentum minus initial: $-4 - 2 = -6$ .
Evaluate the constraint: "Total mass must be $\le 0.50\,\text{kg}$ ." Is it a constraint or criterion?

Constraint. Mass limit is a restriction, not a performance goal.
What is a design criterion in a collision-related engineering problem?

A required performance goal the design must achieve. Criteria define what the design must accomplish successfully.
What formula relates momentum to mass and velocity for evaluating collisions?

$p = mv$ . Momentum is the product of an object's mass and velocity.
Which statement defines a perfectly inelastic collision in terms of motion after impact?

Objects stick together and move as one. Maximum kinetic energy is lost in this collision type.
Choose the better design for lower force: A stops in $0.10\,\text{s}$ , B stops in $0.40\,\text{s}$ (same $\Delta p$ ).

Design B. Longer collision time (B) means lower average force for same momentum change.
Which option is a valid constraint statement for a crash barrier design?

Total mass of the barrier must be at most a specified value. Constraints set limits on design parameters.
Which option best indicates a design reduced damage by lowering energy transferred to the object?

The object has a smaller change in kinetic energy after impact. Less kinetic energy change means less energy absorbed by object.
Calculate momentum: For $m=0.40\,\text{kg}$ and $v=3.0\,\text{m/s}$ , what is $p$ ?

$1.2\,\text{kg}\cdot\text{m/s}$ . Using $p=mv$ : $0.40\times 3.0=1.2\,\text{kg}\cdot\text{m/s}$ .
What is a design constraint in a collision-related engineering problem?

A limit on materials, cost, size, time, or safety. Constraints set boundaries that cannot be exceeded.
What is a controlled variable in a collision design test?

A factor kept constant so results reflect only the design change. Controls ensure only the tested design feature affects results.

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