HS-PS2-4: Calculating Gravity and Electric Forces
Also called NGSS HS-PS2-4 · Topic: Forces and Interactions · Physical Science
The Official Wording
Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects.
Clarification statement: Emphasis is on both quantitative and conceptual descriptions of gravitational and electric fields.
Assessment boundary: Assessment is limited to systems with two objects.
NGSS Lead States, 2013 · Read it on nextgenscience.org · checked October 15, 2026
What HS-PS2-4 Means in Plain English
High school students apply Coulomb's law and Newton's law of gravitation to calculate the force between two objects. They see that both forces grow with charge or mass and weaken with the square of distance, so doubling the gap leaves one quarter of the force.
Problems stay with just two objects, such as two charged spheres or a planet and a moon, and students describe the fields as well as the numbers. This builds on MS-PS2-4 and leads to modeling field energy in HS-PS3-5.
HS-PS2-4 I Can Statements
- I can calculate the electric force between two charges.
- I can calculate the gravitational force between two masses.
- I can predict how a force changes when the distance doubles.
HS-PS2-4 Worked Example
A worked problem with two charged foil balls, plus a quick look at how weak gravity is between them.
Two 2.0 g foil-covered balls each carry +5.0 × 10⁻⁸ C from a Van de Graaff generator. The centers are 0.050 m apart. Find the electric force, the force at 0.10 m, and the gravity between them.
- Write Coulomb's law with k = 9.0 × 10⁹ N·m²/C².F = k·q₁·q₂ ÷ r²
- Put in both charges and the 0.050 m distance.F = (9.0 × 10⁹)(5.0 × 10⁻⁸)² ÷ (0.050)²
- Work it out. Both charges are positive, so the balls repel.F = 9.0 × 10⁻³ N, a repulsion
- Double the distance to 0.10 m. The bottom of the fraction grows four times.F = 2.25 × 10⁻³ N, one quarter as strong
- Now use G = 6.67 × 10⁻¹¹ N·m²/kg² for the 0.0020 kg balls at 0.050 m.Gravity ≈ 1.1 × 10⁻¹³ N, about 80 billion times weaker
Check it: Doubling the distance should cut the force to a quarter, and 9.0 ÷ 2.25 = 4, so the two answers agree.
Common Mistakes with HS-PS2-4
Forgetting to square the distance
Doubling the distance and halving the force
Try this: The distance is squared in both laws, so doubling it divides the force by four, and tripling it divides by nine.
Skipping unit conversions
Putting in 5 cm as 5 and 50 nC as 50
Try this: Convert to meters, kilograms and coulombs before calculating, since the values of k and G only work with SI units.
Thinking the bigger object pulls harder
“Earth pulls on the Moon more than the Moon pulls on Earth.”
Try this: Both objects feel the same size force in opposite directions. The lighter one just accelerates more because its mass is smaller.
Where HS-PS2-4 Fits
Practice HS-PS2-4
Quick Check
- Two charges are moved three times farther apart. What happens to the force?
- Why do small objects show electric forces we notice but no gravity we notice?
- One of two like charges is switched to the opposite sign. What changes?