Final answer:
To experimentally determine the gravitational mass of an object, a student can use a pendulum or a torsion balance experiment. Both methods involve measuring the effects of gravity and calculating the mass based on known physical properties and forces.
Step-by-step explanation:
To determine the gravitational mass of an object without using a scale, a student can conduct either a pendulum experiment or a torsion balance experiment, both of which involve the concept of torque. In the pendulum experiment, the student would set up a simple pendulum, measure its period of oscillation, and use it to calculate the acceleration due to gravity, g. By knowing the length of the pendulum and the acceleration due to gravity, the mass of the pendulum bob can be derived.
In the torsion balance experiment, similar to Cavendish's historic gravitational experiment, two small masses (m) are suspended from a wire, and their gravitational attraction to two larger, stationary masses (M) causes a torsional twist in the wire. By measuring the angle of twist and knowing the properties of the wire, the gravitational force and hence the masses can be determined. In both experiments, careful observations, measurements, and calculations allow a student to determine the unknown mass.