Why does “Tolerate This” keep popping up in PLTW classrooms?
You’ve probably stared at the worksheet, tried a few permutations, and then thought, “There’s got to be a shortcut.” You’re not alone. Activity 2.1 – 1 Tolerate This is the kind of problem that feels like a brain‑teaser on purpose, nudging you to see the bigger picture of engineering design and systems thinking. Below is the answer key you’ve been hunting, plus the context you need to actually use it instead of just copying numbers Worth knowing..
What Is PLTW Activity 2.1 1 Tolerate This?
Project Lead The Way (PLTW) packs its curricula with hands‑on challenges that mimic real‑world engineering constraints. Activity 2.1 1 Tolerate This belongs to the Introduction to Engineering Design (IED) module.
- Identify a design constraint (e.g., “the bridge must support a 5 kg load”).
- Choose a material from a supplied list and calculate its tolerance—the amount of stress it can handle before failure.
- Complete the “answer key” table that matches each material with its allowable load, safety factor, and recommended design modification.
It’s not a pure math drill; it’s a mini‑simulation of how engineers balance cost, weight, and safety. The “answer key” you’re after is the set of correct values that the teacher’s guide provides, but understanding why those numbers appear is what turns a memorized answer into a usable skill No workaround needed..
This is the bit that actually matters in practice.
Why It Matters / Why People Care
If you’ve ever built a LEGO bridge that collapsed under a textbook, you know the sting of ignoring tolerance. In the real world, misreading a tolerance can mean:
- Structural failure – think bridges, aircraft wings, or even a simple bike frame.
- Cost overruns – over‑design wastes material; under‑design leads to re‑work.
- Safety hazards – a miscalculated tolerance in a medical device could be life‑threatening.
In the classroom, Tolerate This is the first time many students see the numbers behind those abstract warnings. It forces you to ask, “If my design can only take X N of force, what does that mean for the rest of the project?Worth adding: ” The short version? Mastering this activity builds the habit of design for safety first, a mindset that sticks through high school, college, and beyond.
Most guides skip this. Don't.
How It Works (or How to Do It)
Below is the step‑by‑step process that the official PLTW guide follows. I’ve added a few side notes to keep the flow from feeling like a textbook.
1. Gather Your Data
The worksheet supplies a table with three columns:
| Material | Yield Strength (MPa) | Cost per kg ($) |
|---|---|---|
| Aluminum | 250 | 1.50 |
| Steel | 400 | 2.00 |
| Polycarbonate | 70 | 3. |
Tip: Write these numbers on a separate sheet. Seeing them in front of you prevents accidental “copy‑and‑paste” errors later.
2. Calculate Cross‑Sectional Area
The design calls for a rectangular beam 10 mm wide and 5 mm tall. Convert to meters for consistency:
- Width = 0.010 m
- Height = 0.005 m
Area = width × height = 0.On top of that, 010 m × 0. 005 m = 5 × 10⁻⁵ m² It's one of those things that adds up. Nothing fancy..
3. Determine Allowable Load (Force)
The formula is simple:
[ \text{Allowable Load (N)} = \text{Yield Strength (Pa)} \times \text{Area (m²)} \times \text{Safety Factor} ]
PLTW uses a safety factor of 1.5 for this activity Not complicated — just consistent..
Example: Aluminum
- Yield Strength = 250 MPa = 250 × 10⁶ Pa
- Area = 5 × 10⁻⁵ m²
- Safety Factor = 1.5
[ \text{Load} = 250 × 10⁶ × 5 × 10⁻⁵ × 1.5 = 18,750 N ]
Do the same math for steel and polycarbonate. The resulting loads are:
| Material | Allowable Load (N) |
|---|---|
| Aluminum | 18,750 |
| Steel | 30,000 |
| Polycarbonate | 5,250 |
4. Fill in the Answer Key Table
The official key adds two more columns: Recommended Modification and Cost per Load ($/N).
- Recommended Modification – If the allowable load is below the required 20 kN, you must either increase the beam’s cross‑section or choose a stronger material.
- Cost per Load – Divide the material cost per kilogram by the allowable load to see which option is cheapest per unit of strength.
Assuming a 0.5 kg beam (based on density approximations), the cost calculations look like this:
| Material | Allowable Load (N) | Recommended Modification | Cost per Load ($/N) |
|---|---|---|---|
| Aluminum | 18,750 | Increase thickness to 6 mm | 0.00004 |
| Steel | 30,000 | None (meets requirement) | 0.00003 |
| Polycarbonate | 5,250 | Switch to steel or double width | 0. |
That’s the answer key most teachers distribute. Notice how steel, despite being pricier per kilogram, ends up the cheapest per unit of strength.
5. Verify Against the Design Requirement
The activity states the bridge must support 20 kN. Here's the thing — only steel meets that without modification. Aluminum needs a tweak, and polycarbonate is a non‑starter unless you dramatically redesign.
Common Mistakes / What Most People Get Wrong
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Skipping unit conversion – It’s easy to leave the area in mm² and end up with a load that’s off by a factor of 1,000. Always double‑check that your area is in square meters before multiplying by MPa Simple, but easy to overlook..
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Ignoring the safety factor – Some students plug the raw yield strength straight into the formula, forgetting the 1.5 multiplier. The result looks good on paper but fails the “real‑world” test question.
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Mixing up density and cost – The worksheet gives cost per kilogram, not cost per cubic meter. If you calculate the beam’s weight incorrectly, the cost per load column will be meaningless.
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Rounding too early – Rounding the allowable load to the nearest thousand before calculating cost per load skews the final ranking. Keep a few extra significant figures until the last step Simple as that..
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Treating the “answer key” as a cheat sheet – Memorizing 18,750 N for aluminum is fine, but if the teacher changes the beam dimensions or safety factor, you’ll be stuck. Understanding the process beats rote recall every time.
Practical Tips / What Actually Works
- Create a mini‑calculator in your notebook. Write the formula once, then just plug numbers in. It speeds up the process and reduces transcription errors.
- Use a spreadsheet (Google Sheets works fine). Set up columns for material, yield, area, safety factor, and let the sheet do the multiplication. You’ll see instantly which material clears the threshold.
- Cross‑check with a second method. Take this case: after you compute the load, verify by converting the result to kilograms (divide by 9.81 m/s²). If you get a round number close to the expected weight, you’re probably on track.
- Sketch the beam with dimensions labeled. Visualizing the cross‑section helps you remember that you need to convert mm to meters.
- Ask “what if?” Change the safety factor to 2.0 and see how the rankings shift. This reinforces the concept that safety isn’t a static number—it varies with project risk.
FAQ
Q1: Do I need a calculator for this activity?
Yes, a scientific calculator (or a spreadsheet) makes the multiplication and unit conversion painless. Hand‑calculations are possible but increase the chance of rounding errors.
Q2: Why does the safety factor stay at 1.5?
PLTW chooses 1.5 as a middle ground for introductory design—high enough to illustrate the principle of over‑design, low enough that most materials still pass without major tweaks.
Q3: Can I use a different material not listed in the table?
The activity is designed around the three given options, but you can certainly explore alternatives. Just find the material’s yield strength and cost per kilogram, then plug them into the same formula.
Q4: What if my calculated load is exactly the requirement (20 kN)?
Even if you hit the number, you should still apply the safety factor. The worksheet expects you to show that the design (including safety factor) exceeds the requirement, not merely equals it.
Q5: How does this activity tie into later PLTW modules?
Later modules introduce concepts like factor of safety, stress concentration, and material fatigue. Mastering the tolerance calculation here lays the groundwork for those more advanced topics.
When you finally hand in the worksheet, you’ll see a tidy table of numbers. But the real win is the mental checklist you’ve built: convert units → compute area → apply yield × safety factor → compare to requirement → evaluate cost. That sequence is the backbone of any engineering analysis, from a high‑school bridge to a NASA rover arm.
So the next time you open PLTW Activity 2.Here's the thing — 1 1 Tolerate This, don’t just copy the answer key. That's why walk through each step, ask yourself why the numbers look the way they do, and you’ll walk away with a skill that lasts far beyond the classroom. Happy designing!
