Mechanics
Fall toward M
Watch the ball accelerate toward central mass M — stronger when closer (inverse-square).
Fall toward M — interactive Mechanics simulation. Watch the ball accelerate toward central mass M — stronger when closer (inverse-square). Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Inverse-square gravitation
Newtonian gravity falls off as 1/r². A body released near a central mass accelerates faster as it gets closer.
Unlike uniform g near Earth’s surface, the gravitational field of a point mass strengthens as distance shrinks. Radial fall under 1/r² gravity is a key step toward understanding orbits and escape speed.
- F = GMm/r²
- g(r) = GM/r²
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
A probe is released from rest and falls straight toward a central mass under inverse-square gravity. As it drops from radius 3.0 m to 2.0 m to 1.0 m, how does its speed change?
Predictions to weigh
- It gains speed at a steady rate, just like a ball dropped near Earth's surface.
- It gains speed faster and faster — the pull grows stronger as it gets closer.
- It slows down as it approaches, because the central mass repels fast-movers.
Variable roles
What you set:
- Release Radius r₀ (m)
- Radius r (m)
What you measure:
- Escape Speed at r (m/s)
- Fall Speed (m/s)
How the investigation runs
- Open the grav-fall preset. A single probe sits at rest a distance r₀ = 3.5 m from the central mass at the center of the canvas.
- Confirm the r-probe (distance) and speed probe are both attached to the probe body before you run anything.
- Run the simulation and pause it as the probe passes r = 3.0 m, then 2.0 m, then 1.0 m, reading the speed probe at each radius.
Governing equation
Gravitational Potential Energy — PE = −m·GM / r
As the probe falls inward, r shrinks and this (negative) potential energy becomes more negative, releasing energy that reappears as kinetic energy — which is why the probe keeps speeding up rather than falling at a steady rate.
Escape Speed — v_esc = √(2GM / r)
The speed a body would need at radius r to just barely escape the central mass. A probe dropped from rest starts with negative total energy, so its fall speed stays below this value at every radius — it is bound, not escaping.
What the printable worksheet asks students to work out
- The probe falls the same 0.5 m from 3.5→3.0 m and again from 1.5→1.0 m, yet it gains far more speed over the inner interval. Use your data to explain why equal distances do not give equal speed gains here (unlike free fall at constant g).
- For each row, compare your measured fall speed to the escape speed at that same radius. The fall speed is always smaller — connect this to the fact that the probe started from rest (its total energy is negative, so it stays bound).
Where this shows up beyond the lab
- Near Earth's surface we use v = √(2g·Δh) with a constant g. Explain why that formula fails here, and what quantity replaces the constant g as the probe moves inward.
- The idealized formula v = √(2GM(1/r − 1/r₀)) blows up to infinity as r → 0. The real simulation instead pins the probe just outside the center. What physical reason (and what modeling choice) keeps the speed finite?
- AP Physics 1 — Unit 6: Energy and Momentum of Rotating Systems
- AP Physics C: Mechanics — Unit 2: Force and Translational Dynamics
- IB Physics — A.4 Rigid body mechanics
- IB Physics — D.1 Gravitational fields
- General High School Physics — Rotation, gravitation & orbits
- NGSS High School Physics — Gravitational and electrostatic forces
- Middle School Physical Science — Gravity between objects
- Welcome to Grav Fall
- Select the probe
- Press Play
- Falling inward
- Open the data
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.
Newton's Law of Universal Gravitation