The bus in the preceding problems is 70 feet long, according to its passengers and driver. Show

step 1 So let's first write down the equation for length contraction. So if L is the measured length of

The bus in the preceding problems is 70 feet long, according...

Key Concepts

Reference Frame

A reference frame is a coordinate system or viewpoint from which observations and measurements of physical phenomena are made. In the context of the problem, the bus’s proper length is measured in its own moving inertial frame, while an observer on a fixed planet measures the bus from another inertial frame, resulting in relativistic effects such as length contraction.

Lorentz Factor

The Lorentz factor, often denoted by the symbol ? (gamma), quantifies the amount of time dilation and length contraction that occurs at relativistic speeds. It is defined as 1 divided by the square root of (1 minus the square of the relative velocity over the speed of light squared). This factor becomes significantly greater than 1 as the relative velocity approaches the speed of light, leading to marked differences in measurements between inertial frames.

Length Contraction

Length contraction is a phenomenon predicted by special relativity which states that an object in motion relative to an observer will appear shorter along the direction of motion compared to its proper length measured in its rest frame. This concept is crucial for explaining why an object like the bus, which is 70 feet long in its own frame, can appear significantly shorter (in this case, slightly less than 10 feet) as seen from a different, stationary frame.

Special Relativity

Special relativity is the branch of physics that addresses how measurements of space and time differ for observers in different inertial frames, especially when those frames are in relative motion at speeds close to the speed of light. It introduces concepts such as time dilation and length contraction, which account for the varying observations of time intervals and distances when moving at high velocities.

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