Cavendish-Experiment: die Erde wiegen (3D)
About this app
Die Torsionswaage von 1798: Zwei große Bleikugeln ziehen einen 1,8 m langen Stab mit kleinen Kugeln um wenige Millimeter zur Seite. Kugeln umlegen, die langsame Schwingung durchs Fernrohr ablesen, aus Ausschlag und Schwingungsdauer G berechnen und daraus Masse und Dichte der Erde. Die kleine Masse kürzt sich heraus.
With explain mode: an AI tutor walks you through the app, points out what matters in the scene and answers your questions.
What it is about
In 1797/98 Henry Cavendish was the first to measure in a laboratory how strongly two masses attract each other. His torsion balance, based on an idea by John Michell, is a 1.8 m rod with two small lead balls on a thin wire. Two large lead balls of 158 kg each pull it aside with about 1.5·10⁻⁷ newtons until the twisted wire holds against them. The deflection and the period give the gravitational constant G, and from it the mass and mean density of the Earth. Cavendish obtained 5.448 times the density of water; today’s value is 5.514.
What the app shows
The app shows the balance in its mahogany case, the large balls on a rotating beam and the telescopes through which Cavendish read it from outside. You swing the large balls and watch the slow oscillation in time lapse, through the telescope and in the chart. Like Cavendish, the app evaluates three turning points: rest position, period and from them G = 2π²Lr²θ/(MT²). A panel goes on to the mass of the Earth, about 6·10²⁴ kg, and compares its density with water, granite and iron.
What you can try
Change the mass of the small balls: the deflection grows, the swing gets slower, the measured G stays the same because m cancels. With the stiffer wire the balance swings in 7.5 instead of 15 minutes and the deflection becomes four times smaller. Switch off the 40× magnification and see how tiny the motion really is. The readings scatter by about one percent, as on a vernier.
Frequently asked questions
- What did Cavendish measure in 1798?
- Cavendish used a torsion balance to measure the attraction between lead balls and derived the mean density of the Earth from it: 5.448 times that of water. He spoke of “weighing the world”. He did not state the gravitational constant G; his data imply G ≈ 6.74·10⁻¹¹ m³/(kg·s²), today 6.674·10⁻¹¹.
- How does a torsion balance work?
- A horizontal rod hangs from a thin wire. A sideways force at the rod ends twists the wire until its restoring torque balances the force. The stiffness of the wire is found from the rod’s period of oscillation. This way forces of less than a millionth of a newton can be measured.
- How do you get from G to the mass of the Earth?
- Every body at the Earth’s surface falls with g = G·M/R². With g = 9.81 m/s², the Earth’s radius R = 6371 km and G, the Earth’s mass is M = g·R²/G ≈ 6·10²⁴ kg. Divided by the volume this gives a mean density of about 5.5 g/cm³, twice that of surface rock.
- What can I try in this app?
- You swing the large balls, read the oscillation through the telescope and let the app evaluate G from three turning points. You change masses, distance, wire and time lapse and go on in the Earth panel to the Earth’s mass and density. Explain mode demonstrates the experiment step by step.
Subject: Physics
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