Two identical scientific probes, Probe A and Probe B, are drifting far from any massive bodies. Probe A is equipped with an internal reference frame that it defines as “at rest.” Probe B is moving past Probe A in the +x-direction at a constant speed of 3.0ms−1 as measured by instruments on Probe A.
A small calibration sphere of mass 0.40kg is ejected gently from the interior of Probe B so that, according to observers inside Probe B, the sphere is released from rest (it simply floats just outside an open hatch).
Answer the following questions using clear, complete sentences and any necessary equations.
(a) Describe how it is possible for observers in the two probes to disagree on the speed of the sphere while agreeing on its mass.
(b) Calculate the speed of the sphere as measured by observers on Probe A immediately after the release.
(c) Using appropriate reasoning, explain why the numerical value of the sphere’s translational kinetic energy is different for the two groups of observers even though the physical situation is identical.
(d) Discuss how the law of conservation of energy can remain valid in each probe’s frame of reference even though the calculated kinetic energies are not the same between frames.