Introduction

In 1665, Isaac Newton proposed that all bodies attract each other, according to his famous law: F=Gm₁m₂/r² where G is the gravitational constant, m₁ and m₂ are the masses of the two bodies and r is the distance that separates their centers of mass. In 1798, Henry Cavendish constructed a device to measure G, using a torsional balance and masses. In this experiment, we will use the method of Cavendish to measure G.

Equipment

• Leybold Gravitation Torsion Balance, including:
•  Torsion balance
•  Instruction manual
•  Two massive lead spheres
•  He-Ne laser
•  Rulers and a watch

Read the instruction manual and set up the torsion balance.

CAUTION: Remember to always tighten the locking screws whenever you move the apparatus. Level the balance so that the torsion pendulum hangs freely.

Allow the system to rest for at least a few hours to allow all vibrations and oscillations to die off (this can be sped up by damping the motion with a magnet, as described in the manual). This experiment requires patience, and care not to bump into the table! Also, avoid leaving the apparatus in direct sunlight or a drafty area, as the torsion pendulum is very sensitive to motion induced by environmental effects.

Devise a clever means of measuring the positions of the masses in the experiment; the values provided in the notebook are approximate.

Use the laser and lens to project the orientation of the mirror on a distant wall. Why is the lens used? Without the large lead masses, verify the zero-point adjustment. Rotate the torsion head slightly if necessary.

Place the large masses in the holders and in one extreme position (just against the glass), and allow the pendulum to come to rest in equilibrium. At time t = 0, rotate the large masses to the opposite extreme position and measure the position of the reflected laser spot on the distant wall as a function of time. Determine G from your data (including a careful assessment of errors), compare with the accepted value of 6.673x10^-11m³kg^-1s^-2 and discuss any discrepancies. Use both the ``end-displacement method'' (measure the position every 30 seconds or so for at least 4-5 complete oscillations, which should take 40-50 minutes) and the ``acceleration method'' (measure the position as many times as possible during the first quarter of the first oscillation).

In order to leave the experiment undisturbed in the lab room, you might want to turn the laser on and off with an extension cord leading out of the room. Then you could leave the room, let the apparatus settle, then return, turn the laser on, and note the position of the spot, all without re-entering the lab room.

In your report, derive the formulas for G given in the manual. You might want to consult an introductory physics textbook like
Halliday, Resnick and Walker's Fundamentals of Physics
to refresh your memory on the laws governing the torsion balance.