Pltw 1.1.6 Compound Machine Design Answer Key

PLTW 1.1.6 Compound Machine Design – Guide and Sample Answer Key

Project Lead The Way (PLTW) introduces students to engineering concepts through hands‑on activities. In unit 1.1.6 learners are asked to design a compound machine that can lift a specified load using a combination of simple machines. The goal is to apply principles of mechanical advantage, work, and energy while practicing the engineering design process. Below you’ll find a detailed walk‑through of the activity, the key concepts you need to master, and a sample answer key that illustrates how a successful solution might look. The sample is original and meant to help you check your reasoning; it is not a direct copy of any proprietary PLTW material.

Introduction

The PLTW 1.1.6 challenge asks you to create a compound machine that meets a set of performance criteria (e.g., lift a 5 kg weight at least 0.30 m using no more than two motors or a single hand‑crank). To succeed you must:

1. Identify which simple machines (lever, pulley, wheel‑and‑axle, inclined plane, wedge, screw) will give you the greatest mechanical advantage.
2. Sketch a design that combines at least two of those simple machines. 3. Calculate the overall mechanical advantage (MA) and verify that the input force required is within the allowed limits.
3. Build a prototype, test it, and iterate based on the results.

Understanding the underlying physics and following a systematic design process are the keys to earning full credit. The sections that follow break each of those steps down and provide a sample solution you can compare against your own work.

Overview of the Activity

The activity is deliberately open‑ended; there is no single “right” machine. What matters is that you can justify your choices with calculations and test data.

Understanding Compound Machines

A compound machine is simply two or more simple machines linked so that the output of one becomes the input of the next. The total mechanical advantage is the product of the individual advantages:

[ \text{MA}_{\text{total}} = \text{MA}_1 \times \text{MA}_2 \times \dots \times \text{MA}_n ]

Where each simple machine’s MA is defined as:

When you combine machines, remember that friction and material flexibility will reduce the ideal MA. In your report you should note the actual MA measured from your test runs and compare it to the ideal value.

Step‑by‑Step Design Process

Below is a concise roadmap you can follow while working on 1.1.6. Each step includes the key deliverables that PLTW typically looks for in the engineering notebook.

1. Define the Problem & Gather Requirements

• Write a clear problem statement (e.g., “Design a machine that lifts a 5 kg mass 0.30 m using at most one hand‑crank”).
• List all constraints (materials, time, weight, safety).

2. Research Simple Machines

• Review the MA formulas above.
• Decide which two (or more) machines will give you the needed advantage while staying within the material budget.
• Sketch at least three concept ideas.

3. Choose a Concept & Create a Detailed Sketch

• Draw a labeled diagram showing each simple machine, the direction of force, and where the load attaches.
• Indicate dimensions (arm lengths, pulley radii, gear ratios) that you will use for calculations.

4. Calculate Ideal Mechanical Advantage

• Compute MA for each subsystem.
• Multiply to obtain MA_total.
• Determine the ideal input force:

[ F_{\text{input, ideal}} = \frac{F_{\

4. Calculate Ideal Mechanical Advantage (Continued)

[ F_{\text{input, ideal}} = \frac{F_{\text{output}}}{ \text{MA}_{\text{total}} } ]

5. Select Materials & Build a Prototype

• Based on your calculations, select appropriate materials for each component. Consider strength, weight, and cost.
• Construct a physical prototype of your compound machine. Document the construction process with photographs and notes.

6. Test & Analyze Results

• Conduct multiple test runs with the chosen load. Record the input force required to lift the load.
• Calculate the actual MA using the formula:

[ \text{MA}{\text{actual}} = \frac{F{\text{input, measured}}}{F_{\text{output}}} ]

• Compare the actual MA to the ideal MA. Identify the sources of error (friction, material flexibility, measurement inaccuracies). Quantify the difference between the ideal and actual MA.

7. Iterate & Improve

• Based on your analysis, identify areas for improvement. This might involve adjusting dimensions, selecting different materials, or modifying the design.
• Revise your design and repeat steps 5 and 6 until you achieve the desired performance.

Example Design: The Lever-Pulley Lift

Let’s illustrate the process with a simple example: a machine designed to lift a 5 kg mass 0.30 m using a hand-crank. We’ll combine a lever and a fixed pulley.

1. Define Problem & Requirements: Lifting a 5 kg mass 0.30 m vertically using a hand-crank. Constraints: Materials – wood and rope; Time – 10 hours; Weight – 1 kg maximum for the entire machine.

2. Research Simple Machines: We’ll use a lever (MA = Effort Arm / Load Arm) and a fixed pulley (MA = 1). A lever allows us to amplify force, and the pulley changes the direction of force.

3. Choose Concept & Sketch: We’ll design a lever system with a fixed pulley attached to the end of the lever arm. The load (5 kg mass) will be attached to the load arm. A sketch would show the lever, pulley, rope, and the 5 kg mass. Dimensions would be estimated – for example, a lever arm of 0.5 m and a load arm of 0.1 m.

4. Calculate Ideal Mechanical Advantage: MA_lever = 0.5 m / 0.1 m = 5. MA_pulley = 1. MA_total = 5 * 1 = 5. Ideal Input Force = 5 kg * 9.8 m/s² / 5 = 9.8 N.

5. Select Materials & Build Prototype: We’d select a sturdy piece of wood for the lever and strong rope for the pulley system. The prototype would be constructed, with careful attention to ensuring the lever pivots smoothly and the pulley is securely attached.

6. Test & Analyze Results: During testing, we’d measure the force required to lift the 5 kg mass. Let’s say we measured an input force of 10 N. MA_actual = 10 N / 5 kg * 9.8 m/s² = 2. The difference between the ideal MA (5) and the actual MA (2) is significant. This discrepancy is likely due to friction in the lever pivot and the rope’s resistance.

7. Iterate & Improve: To improve the design, we could reduce the friction in the lever pivot by applying a lubricant. We could also use a rope with a smaller diameter to reduce friction. We would then repeat steps 5 and 6 to evaluate the revised design.

Conclusion: Designing a compound machine is a systematic process that requires careful consideration of simple machines, mechanical advantage, and potential sources of error. By meticulously following the design process, analyzing test results, and iterating on the design, engineers can create efficient and effective machines that meet specific requirements. Understanding the interplay between ideal and actual mechanical advantage is crucial for optimizing performance and achieving desired results. Furthermore, documenting the entire process through detailed engineering notebooks is essential for demonstrating a thorough understanding of the design principles and the engineering methodology.