A research capsule drifting in deep space far from massive bodies carries a small drone equipped with a camera. At time t=0, the drone releases a metallic sphere inside the capsule’s transparent cabin. The sphere is initially at rest relative to the capsule’s interior wall. Over the next 8.0 s, the drone’s camera records the sphere moving toward the rear wall of the cabin with a steadily increasing speed, covering 2.4 m in that interval. Assume no significant gravitational or magnetic forces act on the sphere, and that air resistance inside the cabin is negligible.
(a) Using the recorded displacement of the sphere, determine its average acceleration relative to the capsule over the 8.0 s interval.
(b) Discuss whether the capsule’s reference frame can be considered inertial during the observation period. Provide quantitative reasoning that incorporates your result from part (a).
(c) Propose a method the crew could use, relying only on simple equipment already aboard, to measure the capsule’s linear acceleration without looking outside. Outline the procedure and the principle behind it.
(d) Explain how your proposed method would distinguish between true acceleration of the capsule and the presence of an unnoticed external force directly on the sphere itself.