Fan Cart Physics Gizmo Answer Key
A fan cart, also known as a fan cart physics gizmo, is a classic laboratory apparatus that demonstrates the principles of forces, motion, and equilibrium. By varying the fan’s speed, the cart’s mass, or the track’s inclination, students can observe how these factors influence acceleration, velocity, and terminal speed. Typically, the cart is equipped with a small electric fan that propels it along a track when powered. The following answer key explains the expected outcomes, calculations, and conceptual insights for common fan cart experiments Simple, but easy to overlook. Which is the point..
Introduction
The fan cart experiment is a cornerstone in introductory physics because it visualizes Newton’s laws in a tangible way. The cart’s motion is governed by Newton’s Second Law (F = ma) and the Law of Conservation of Energy when friction and air resistance are considered. In a typical lab, students are asked to:
Not obvious, but once you see it — you'll see it everywhere Nothing fancy..
- Measure the cart’s acceleration and velocity at different fan speeds.
- Determine the relationship between fan speed and terminal velocity.
- Investigate how adding mass affects the cart’s motion.
- Explore the role of friction and air resistance.
Below, we provide a detailed answer key that covers the expected results, calculations, and conceptual explanations for each of these tasks. The answers assume a standard fan cart setup with a 12 V DC fan, a 1 m track, and a mass range of 50–200 g.
1. Acceleration and Velocity at Different Fan Speeds
Expected Results
| Fan Voltage | Acceleration (m/s²) | Final Velocity (m/s) |
|---|---|---|
| 6 V | 0.Think about it: 8 ± 0. But 05 | 1. Worth adding: 2 ± 0. 07 |
| 9 V | 1.4 ± 0.07 | 2.0 ± 0.In practice, 09 |
| 12 V | 2. On top of that, 1 ± 0. Here's the thing — 10 | 3. 0 ± 0. |
Calculations
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Force from the fan
The fan produces a thrust force (F_{\text{fan}}) proportional to the square of the fan speed, which itself scales linearly with voltage for a DC fan. Empirically, we can model: [ F_{\text{fan}} = kV^2 ] where (k) is a constant determined by calibration Turns out it matters.. -
Net force
Assuming negligible friction and air resistance at low speeds: [ F_{\text{net}} \approx F_{\text{fan}} ] -
Acceleration
Using Newton’s second law: [ a = \frac{F_{\text{net}}}{m} ] For a cart mass (m = 0.15) kg and a measured acceleration of 1.4 m/s² at 9 V, the implied thrust is: [ F_{\text{fan}} = a \times m = 1.4 \times 0.15 = 0.21\ \text{N} ] -
Velocity
With constant acceleration over a distance (s = 0.5) m (half the track length to avoid hitting the end), the final speed is: [ v = \sqrt{2as} = \sqrt{2 \times 1.4 \times 0.5} \approx 1.18\ \text{m/s} ] This matches the experimental value within error.
Conceptual Insight
- Nonlinear relationship: The fan’s thrust increases with the square of voltage, leading to a nonlinear increase in acceleration.
- Energy transfer: Electrical energy supplied to the fan is converted into kinetic energy of the cart. The efficiency depends on fan design and air resistance.
2. Fan Speed vs. Terminal Velocity
Expected Trend
As fan speed increases, the cart’s terminal velocity rises but eventually levels off due to air resistance and friction. A typical plot shows a steep rise from 0 V to ~8 V, followed by a gradual plateau Small thing, real impact. Less friction, more output..
Calculations
At terminal velocity (v_t), the net force is zero: [ F_{\text{fan}} = F_{\text{drag}} + F_{\text{friction}} ]
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Drag force: (F_{\text{drag}} = \frac{1}{2}\rho C_d A v_t^2)
- (\rho) = air density (~1.2 kg/m³)
- (C_d) = drag coefficient (~0.8 for a rectangular cart)
- (A) = frontal area (~0.02 m²)
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Friction: (F_{\text{friction}} = \mu_k N)
- (\mu_k) = kinetic friction coefficient (~0.05)
- (N) = normal force (~(mg))
Solving for (v_t) gives: [ v_t = \sqrt{\frac{2(F_{\text{fan}} - \mu_k mg)}{\rho C_d A}} ]
Plugging in typical numbers for 12 V (where (F_{\text{fan}} \approx 0.15 \times 9.35 - 0.05 \times 0.35) N) yields: [ v_t \approx \sqrt{\frac{2(0.8 \times 0.In real terms, 8)}{1. 2 \times 0.02}} \approx 3.
This theoretical value aligns closely with the experimentally measured terminal velocity (~3.0 m/s) It's one of those things that adds up..
Conceptual Insight
- Balance of forces: Terminal velocity occurs when the propulsive force equals the sum of resistive forces.
- Scaling laws: Drag scales with (v^2), while friction is constant; thus, at high speeds, drag dominates.
3. Effect of Adding Mass
Experimental Observation
Adding mass to the cart reduces both acceleration and terminal velocity. 4 m/s², and terminal velocity falls to ~2.For a 200 g added mass (total 350 g), acceleration at 12 V drops to ~1.5 m/s.
Calculations
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Acceleration: [ a = \frac{F_{\text{fan}}}{m_{\text{total}}} = \frac{0.35}{0.35} = 1.0\ \text{m/s}^2 ] (actual measured value slightly higher due to reduced friction per unit mass) Easy to understand, harder to ignore. That alone is useful..
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Terminal velocity: [ v_t = \sqrt{\frac{2(F_{\text{fan}} - \mu_k m_{\text{total}}g)}{\rho C_d A}} ] Substituting (m_{\text{total}} = 0.35) kg gives (v_t \approx 2.5) m/s.
Conceptual Insight
- Inertia: Greater mass increases inertia, requiring the same force to achieve the same acceleration.
- Friction scaling: Friction increases linearly with mass, reducing net propulsive force at terminal speed.
4. Role of Friction and Air Resistance
Quantitative Analysis
- Friction coefficient: Measure by placing the cart on a slightly inclined plane and noting the angle at which it just overcomes static friction. Typical (\mu_s) ≈ 0.06.
- Air resistance: Determined by fitting velocity vs. time data to the drag equation. The fitted drag coefficient (C_d) often falls between 0.7 and 0.9 for standard cart shapes.
Experimental Procedure
- Static friction test: Record the minimum angle (\theta) where the cart starts moving. [ \mu_s = \tan(\theta) ]
- Dynamic friction test: Measure the constant deceleration when the fan is turned off; this yields (\mu_k).
Conceptual Insight
- Friction vs. air drag: For short tracks and low speeds, friction dominates. As speed increases, air drag becomes the primary resistive force.
- Energy dissipation: Both friction and drag convert kinetic energy into heat and turbulence, limiting the cart’s speed.
Frequently Asked Questions (FAQ)
| Question | Answer |
|---|---|
| Can I use a different fan? | Accuracy depends on timing resolution; using a photogate or high‑speed camera improves precision. |
| What if the track is not perfectly horizontal? | This occurs when the fan is turned off; the cart decelerates due to friction and drag. Even so, |
| **How accurate is the terminal velocity measurement? On top of that, ** | Not directly; the cart is not isolated. |
| Why does the acceleration sometimes appear negative? | Yes, but you must recalibrate (k) in the thrust equation because fan characteristics differ. ** |
| **Can I use this setup to demonstrate conservation of momentum? On the flip side, collisions with a second cart can illustrate momentum transfer. |
Conclusion
The fan cart physics gizmo offers a hands‑on demonstration of several foundational physics concepts: Newton’s laws, force balance, energy conversion, and the interplay between mass, friction, and air resistance. By systematically varying fan speed, cart mass, and track conditions, students can observe predictable changes in acceleration and velocity that align with theoretical predictions. Day to day, the answer key above provides a comprehensive reference for interpreting experimental data, performing calculations, and deepening conceptual understanding. Whether used in a high‑school laboratory or an introductory university course, the fan cart remains an engaging, low‑cost tool for bringing physics to life Less friction, more output..
