A laboratory experiment measures the attractive force between two identical small spheres whose masses remain unchanged throughout the trial. The magnitude of the force is recorded for several center-to-center separations r. The researcher summarizes the observations in the verbal description below:
• When the separation is 0.20m, the measured force is 1.8×10−8N.
• When the separation is doubled to 0.40m, the force decreases to 4.5×10−9N.
• When the separation is tripled to 0.60m, the force is approximately 2.0×10−9N.
Assume the only significant interaction acting on the spheres is their mutual attraction.
(a) Describe the mathematical relationship suggested by the data between the magnitude of the attractive force F and the separation r. Your description should state whether F varies directly, inversely, or with a specific power of r, and cite at least one pair of data points as evidence.
(b) Use an appropriate pair of data points to calculate the numerical value of the exponent n in a trial relationship of the form F∝r−n. Show your reasoning clearly.
(c) Based on your result in part (b), explain whether doubling the mass of one sphere (while keeping separation r unchanged) would change the exponent n. Justify your answer qualitatively without performing additional numerical calculations.
(d) The student claims that if both sphere masses are simultaneously doubled while the original separations are kept, the constant of proportionality in the force-separation relationship will change but the functional dependence on r will not. Evaluate this claim, citing evidence from the relationship you determined.