Investigating the Invisible: Gravity vs. Electrostatics
Part 1: Engage (Anchoring Phenomenon)
Estimated Time: 15 minutes Materials: Two bar magnets, a balloon, and a small piece of paper.
Observe & Wonder
Think about how a magnet can pick up a paperclip without touching it, or how rubbing a balloon on your hair allows it to stick to a wall. In both cases, there is an invisible force pulling objects together (or pushing them apart). At the same time, an invisible force (gravity) is constantly pulling all of us toward the center of the Earth.
- How do the invisible forces of a magnet or static electricity compare to the invisible force of gravity?
- Can you think of a time when the force of static electricity was stronger than gravity?
- Write down at least two “need to know” questions you have about how these invisible forces work.
Part 2: Explore (Simulation Investigation)
Estimated Time: 30 minutes Materials: Gravity & Electrostatics Simulator
Access the Simulator
Open the Gravity & Electrostatics Simulator. Make sure you can see the sliders for Distance (r), Mass 1 ($m_1$), Mass 2 ($m_2$), Charge 1 ($q_1$), and Charge 2 ($q_2$). Note the buttons for “Single View” and “Compare View” at the top of the simulation.
Investigation 1: Exploring Gravity
- Click the “Single View” button and then the “Gravity” button to focus only on the gravitational force.
- Set $m_1$ and $m_2$ to 1000 kg. Set the distance $r$ to 5.0 m.
- Observe the length and direction of the force vectors (the red arrows). Read the calculated force of gravity ($F_g$) below the canvas.
- Change Mass: Increase $m_1$ to 5000 kg. What happens to the force vectors? Click “Record Data Point”.
- Change Distance: Decrease the distance $r$ to 2.5 m. What happens to the force vectors? Click “Record Data Point”.
- Direction: Try to make the force of gravity push the masses apart (repel). Is this possible? Record your observations.
Investigation 2: Exploring Electrostatics
- Click the “Electrostatics” button to focus only on the electrostatic force.
- Set $q_1$ to 5.0 μC and $q_2$ to 5.0 μC. Set the distance $r$ to 5.0 m.
- Observe the direction of the force vectors. Are the charges attracting or repelling?
- Change Charge: Change $q_2$ to -5.0 μC. What happens to the direction of the force vectors?
- Change Distance: Decrease the distance $r$ to 2.5 m. What happens to the magnitude of the force ($F_e$)?
- Record several data points as you change the charges (both positive and negative) and the distance.
Investigation 3: Compare View
- Click the “Compare View” button to see both gravity and electrostatics at the same time.
- Set $r$ = 5.0 m. Set $m_1$ and $m_2$ to 5000 kg. Set $q_1$ and $q_2$ to 1.0 μC and -1.0 μC.
- Look at the calculated values for $F_g$ and $F_e$. Which force is stronger in this scenario? By how much?
| Trial | $r$ (m) | $m_1$ (kg) | $m_2$ (kg) | $q_1$ (μC) | $q_2$ (μC) | $F_g$ (N) | $F_e$ (N) | Attraction or Repulsion? |
|---|---|---|---|---|---|---|---|---|
| 1 | 5.0 | 1000 | 1000 | 5.0 | -5.0 | |||
| 2 | 2.5 | 1000 | 1000 | 5.0 | -5.0 | |||
| 3 | 5.0 | 5000 | 1000 | 5.0 | 5.0 | |||
| 4 |
Tip: You can use the “Export CSV” button in the simulator to download your full dataset.
Part 3: Explain (Sensemaking)
Estimated Time: 25 minutes
Use your data and observations from the Explore section to answer the following questions:
- Defining the System: Describe the two systems you investigated. What were the interacting objects in each case, and what properties of those objects were responsible for the forces?
- Newton’s Law of Gravitation ($F_g = G\frac{m_1 m_2}{r^2}$): Based on your data, how does the gravitational force change when the mass of one object increases? How does it change when the distance between the objects decreases? Explain why gravity is always an attractive force.
- Coulomb’s Law ($F_e = k\frac{q_1 q_2}{r^2}$): Based on your data, how does the electrostatic force change when the distance between the objects decreases? How do the signs of the charges (positive vs. negative) determine whether the force is attractive or repulsive?
- Comparing Patterns: Compare the mathematical formulas for $F_g$ and $F_e$. What is the mathematical pattern that both forces share when it comes to the distance ($r$) between the objects?
Part 4: Elaborate/Evaluate (Argumentation & Modeling)
Estimated Time: 30 minutes
Constructing an Argument
Using your understanding of Newton’s Law of Gravitation and Coulomb’s Law, construct a scientific argument to answer the following prompt:
Prompt: Imagine an electron (which has a very tiny mass and a negative charge) and a proton (which has a slightly larger mass and a positive charge) are separated by a small distance. Which force—gravitational or electrostatic—will be the dominant force determining how these particles interact?
Your argument must include:
- Claim: A clear statement answering the prompt.
- Evidence: Reference the mathematical structure of $F_g$ and $F_e$ (specifically the constants $G$ and $k$) and the patterns you observed in the simulation.
- Reasoning: Explain why the mathematical formulas predict the outcome you claimed, including how the ratio of the forces behaves independently of the distance $r$.
Teacher Notes & Alignment
- Target NGSS Performance Expectation: HS-PS2-4
- SEPs: Using Mathematics and Computational Thinking (students use formulas to model and predict forces).
- DCIs: PS2.B: Types of Interactions (Newton’s law of universal gravitation and Coulomb’s law provide mathematical models to describe and predict effects).
- CCCs: Patterns (students observe inverse-square relationship across both forces).
- Evidence Statements Addressed:
- 1. Representation (a, b, c): Students define the systems and identify the variables in the formulas for $F_g$ and $F_e$.
- 2. Mathematical Modeling (a): Students use the simulation (which relies on the formulas) to predict forces.
- 3. Analysis (a, b, c, d): Students explain the shared inverse-square pattern, justify why gravity is only attractive (mass is always positive), explain why electrostatics can attract or repel (charges can be positive/negative), and argue which force dominates.