AH Exp – Mechanics 06 – Cavendish-Boys determination of G

Aim – To determine G using the Cavendish-Boys apparatus

Instructions

The two small gold spheres are suspended by a quartz fibre.
They each have a mass of 2 g.
Two larger lead spheres, each of mass 0.6 kg, can be brought close to the smaller spheres.
The gravitational force of attraction causes the smaller spheres to move towards the larger ones and the quartz fibre rotates.
A laser beam is directed at a mirror which is attached to the quartz fibre.
As the fibre rotates, the beam moves, and the angle through which the fibre rotates can be measured from the screen.

▪Click the button to put the large lead spheres in place.

The system takes a few moments to come to rest (in practice this can take a considerable time)

▪Note the angle through which the quartz fibre has rotated. (measured in degrees)

The torque T acting on the cross bar can be found from T=kθ, where k is the torsional constant of the fibre (2.88×10^-11 N m rad^-1), and θ is the angle of rotation in radians.

▪ Calculate T
▪ The torque T is also given by T=Fg x l, where Fg is the gravitational force acting between the small and large sphere and l is the length of the crossbar. (l= 23 mm)
▪ PCalculate the value of Fg

Now Fg= G M m / r² where M and m are the masses of the spheres and r is the distance between the centre of the spheres (70mm).

▪ Calculate a value for G

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