Question

A spacecraft has left the earth and is moving toward Mars. An observer on the earth finds that, relative to measurements made when the spacecraft was at rest, its:

a) Length is shorter
b) Kinetic energy is less than 1/2 ​mv^2
c) Clocks tick faster
d) Rest energy is greater

Answer 1

To an observer on Earth, a spacecraft moving toward Mars at relativistic speeds will appear shorter (length contraction), have relativistic kinetic energy, and experience slower ticking clocks (time dilation); its rest energy remains unaltered.

Step-by-step explanation:

A spacecraft moving away from the Earth toward Mars and traveling at a significant fraction of the speed of light will experience several relativistic effects as observed by an observer on Earth. According to the theory of relativity, the spacecraft will appear to have length contraction, meaning it will look shorter than when at rest. This is due to the relative motion between the spacecraft and the observer. Additionally, the spacecraft's kinetic energy will not fit the classical formula (½ mv2) because relativistic effects become significant at high speeds. Instead, the relativistic formula for kinetic energy should be used. As for time, clocks on the spacecraft will appear to tick slower to the observer on Earth, an effect known as time dilation. The rest energy of the spacecraft remains constant as it is intrinsic to the object; it does not change with the object's state of motion. However, as the spacecraft gains kinetic energy, its total energy, which is the sum of rest energy and kinetic energy, increases.