Evaluate Collision
Design Solutions

Learn to evaluate safety designs using momentum, impulse, and the engineering design process with real-world constraints and criteria.

High School Physics

What Is a Collision?

A collision is an event where two or more objects exert forces on each other over a short time interval. In physics, we analyze collisions using two fundamental quantities:

Momentum

The product of mass and velocity: $ \vec{p} = m\vec{v} $. A measure of how hard it is to stop a moving object.

Impulse

The change in momentum caused by a force over time: $ \vec{J} = \vec{F} \cdot \Delta t = \Delta \vec{p} $. The key to design.

Why Design for Collisions?

Every year, collisions cause injuries and damage. Engineers design solutions that reduce the force experienced during impact. The physics insight is simple but powerful:

But good engineering goes beyond physics: solutions must also satisfy constraints (limits like budget, weight, materials) and criteria (goals like minimizing injury, maximizing durability).

The Engineering Design Process

Evaluating collision design solutions requires understanding the iterative engineering process:

1

Define the problem: identify what needs protection and under what collision conditions.

2

Establish criteria and constraints: set measurable goals (criteria) and non-negotiable limits (constraints).

3

Generate and compare solutions: brainstorm multiple designs, then evaluate each against the criteria.

4

Optimize: refine the best design by trading off competing criteria within constraints.

The Impulse-Momentum Theorem

Conservation of Momentum

In any collision where no external net force acts, total momentum is conserved:

This law tells us the total momentum change is zero, but each object's individual momentum changes by equal and opposite amounts. Design solutions cannot change the total impulse required: they can only control how that impulse is delivered (over what time and across what area).

Criteria vs. Constraints

To evaluate any design, you must distinguish between these two concepts:

Criteria

Desirable outcomes you want to maximize or minimize. They are scored on a spectrum. Example: minimize peak force on the occupant.

Constraints

Hard limits that must be satisfied: pass/fail. A design either meets a constraint or it doesn't. Example: total mass must be under 50 kg.

How to Evaluate a Design

1

List all constraints. Check each design against every constraint. Discard any that fail.

2

Identify the criteria. What physics quantities matter? Peak force, collision time, energy absorbed, cost, weight.

3

Apply the impulse-momentum theorem. Calculate $ F_{ \text{avg}} = \frac{\Delta p}{\Delta t} $ for each design to compare forces.

4

Use a decision matrix. Score each surviving design on every criterion. Weight criteria by importance.

5

Select and justify. Choose the design with the highest weighted score and explain your reasoning with data.

Example 1: Helmet Design

A cyclist's head (mass $ m = 5 $ kg) hits the ground at $ v = 6 $ m/s. Two helmet designs are tested. Which is better?

Helmet A

Stops the head in $ \Delta t = 0.01 $ s. Cost: $30. Mass: 0.4 kg.

Helmet B

Stops the head in $ \Delta t = 0.06 $ s. Cost: $55. Mass: 0.5 kg.

Example 1: Decision Matrix

Constraint: Mass must be under 0.6 kg. Both pass. Budget: under $60. Both pass. Now score the criteria (1-5 scale, 5 = best):

Criterion (weight)	Helmet A	Helmet B
Peak force ($\times 3$)	1 (3,000 N)	5 (500 N)
Cost ($\times 2$)	5 ($30)	3 ($55)
Mass ($\times 1$)	5 (0.4 kg)	4 (0.5 kg)
Weighted total	18	25

Example 2: Car Bumper Redesign

A 1,200 kg car collides with a wall at $ v = 8 $ m/s. Three bumper designs are proposed:

Steel Rigid

$ \Delta t = 0.02 $ s
Cost: $200
Mass: 25 kg

Foam Core

$ \Delta t = 0.10 $ s
Cost: $350
Mass: 18 kg

Crumple Zone

$ \Delta t = 0.25 $ s
Cost: $500
Mass: 30 kg

Applying Constraints and Criteria

Constraint: Budget is $400. The Crumple Zone ($500) exceeds the budget and is eliminated.

Now evaluate the remaining designs:

Criterion (weight)	Steel Rigid	Foam Core
Peak force ($\times 3$)	1	4
Cost ($\times 2$)	5	3
Mass ($\times 1$)	3	5
Weighted total	16	23

Example 3: Egg Drop Challenge

An egg (mass $ m = 0.06 $ kg) is dropped from 3 meters. Using $ v = \sqrt{2gh} $, the impact speed is $ v = \sqrt{2 \times 9.8 \times 3} \approx 7.67 $ m/s.

Real-World Design Solutions

Airbags

Inflate in ~30 ms to cushion the occupant, increasing $ \Delta t $ from ~5 ms to ~100 ms.

Crumple Zones

Front and rear sections deform on impact, extending collision time to ~0.1 - 0.3 s.

Seatbelts

Stretch slightly during impact, distributing force over a wider area and longer time.

Common Mistakes

✕ Confusing Criteria and Constraints

A constraint is pass/fail (budget < $500). A criterion is scored on a scale (lower force is better). Mixing these up leads to wrong evaluations.

✕ Ignoring Constraints

Picking the lowest-force design without checking if it meets all constraints (mass limit, budget, material availability) is invalid engineering.

✕ Thinking Padding "Absorbs" Impulse

Padding does not reduce impulse ($ \Delta p $ is fixed). It extends $ \Delta t $, reducing force. The total momentum change is always the same.

Summary Comparison

Concept	Physics Principle	Design Implication
Momentum	$ \vec{p} = m\vec{v} $	Determines total impulse needed
Impulse	$ \vec{J} = \vec{F} \cdot \Delta t $	Increase $ \Delta t $ to lower $ F $
Conservation	$ \Sigma \vec{p}_i = \Sigma \vec{p}_f $	Cannot eliminate impulse, only manage it
Criteria	Measurable goals	Rank designs by performance
Constraints	Hard limits	Eliminate non-compliant designs first

Question 1 of 5

A car of mass $ m $ traveling at velocity $ v $ crashes and comes to rest. Which design change will most reduce the average force on the occupants?

Since $ F_{\text{avg}} = \frac{\Delta p}{\Delta t} $, increasing $ \Delta t $ directly decreases the average force for the same momentum change. This is the fundamental principle behind crumple zones and airbags.

Question 2 of 5

A design team proposes three helmet prototypes. Prototype C has the lowest peak force but costs $800, exceeding the $500 budget constraint. What should the team do?

Constraints are non-negotiable. Any design that violates a constraint must be eliminated first, regardless of how well it scores on criteria. The team should then rank the remaining designs by their criteria scores.

Question 3 of 5

A $ 0.5 $ kg ball hits a wall at $ 10 $ m/s and bounces back at $ 8 $ m/s. What is the magnitude of the impulse on the ball?

The ball reverses direction, so $ \Delta p = m(v_f - v_i) = 0.5 \times ((-8) - 10) = 0.5 \times (-18) = -9 $ N·s. The magnitude is $ 9 $ N·s. Remember: when an object bounces, you must account for the direction change.

Question 4 of 5

An engineer claims that adding foam padding to a shipping container "absorbs the impulse" and reduces the total momentum change during a drop. Is this claim correct?

The impulse (total momentum change) is determined by the initial and final velocities: $ \Delta p = m\Delta v $. Foam cannot change this. What foam does is extend $ \Delta t $, so the same impulse is delivered with a lower average force. This is a common misconception.

Question 5 of 5

In a decision matrix, Design X scores 4/5 on safety and 5/5 on cost. Design Y scores 5/5 on safety and 3/5 on cost. Safety is weighted $\times 3$ and cost is weighted $\times 1$. Which design has the higher weighted total?

Design X: $ (4 \times 3) + (5 \times 1) = 12 + 5 = 17 $. Design Y: $ (5 \times 3) + (3 \times 1) = 15 + 3 = 18 $. Design Y wins because safety has a higher weight, and its superior safety score outweighs the cost advantage of Design X.

Criterion (weight)	Helmet A	Helmet B
Peak force (\(\times 3\))	1 (3,000 N)	5 (500 N)
Cost (\(\times 2\))	5 ($30)	3 ($55)
Mass (\(\times 1\))	5 (0.4 kg)	4 (0.5 kg)
Weighted total	18	25

Concept	Physics Principle	Design Implication
Momentum	\( \vec{p} = m\vec{v} \)	Determines total impulse needed
Impulse	\( \vec{J} = \vec{F} \cdot \Delta t \)	Increase \( \Delta t \) to lower \( F \)
Conservation	\( \Sigma \vec{p}_i = \Sigma \vec{p}_f \)	Cannot eliminate impulse, only manage it
Criteria	Measurable goals	Rank designs by performance
Constraints	Hard limits	Eliminate non-compliant designs first

Evaluate CollisionDesign Solutions

What Is a Collision?

Why Design for Collisions?

The Engineering Design Process

The Impulse-Momentum Theorem

Conservation of Momentum

Criteria vs. Constraints

How to Evaluate a Design

Example 1: Helmet Design

Example 1: Decision Matrix

Example 2: Car Bumper Redesign

Applying Constraints and Criteria

Example 3: Egg Drop Challenge

Real-World Design Solutions

Common Mistakes

Summary Comparison

Question 1 of 5

Question 2 of 5

Question 3 of 5

Question 4 of 5

Question 5 of 5

Evaluate Collision
Design Solutions