Problem 11 - Applied Physics

Question

An auto mechanic uses a strobe light to time a classic car engine. If the light is held \(0.20 \mathrm{~m}\) from the flywheel and the mechanic's eye is \(0.75 \mathrm{~m}\) from the strobe, how long does it take the light from the strobe to reach the mechanic's eye?

Step-by-Step Solution

Answer

The light takes 2.5 nanoseconds to reach the mechanic's eye.

Step 1: Understand the Problem

The problem involves calculating the time it takes for light to travel from the strobe to the mechanic's eye. We know the distances between the light, the flywheel, and the mechanic's eye, but we need to focus on the direct distance from the strobe to the eye.

Step 2: Determine the Direct Distance

The direct distance from the strobe to the mechanic's eye is simply the linear distance between these two points, which is given as \(0.75 \; \mathrm{m}\). This is because the distance from the light to the flywheel doesn’t affect the path from the strobe to the eye.

Step 3: Recall the Speed of Light

The speed of light in air (and approximated as the same in a vacuum) is \(3 \times 10^8 \; \mathrm{m/s}\). We'll use this constant to calculate the time taken for light to travel the given distance.

Step 4: Calculate the Time Taken

Use the formula \( t = \frac{d}{v} \) to find the time \( t \), where \( d = 0.75 \; \mathrm{m} \) is the distance and \( v = 3 \times 10^8 \; \mathrm{m/s} \) is the speed of light.\[t = \frac{0.75}{3 \times 10^8} = 2.5 \times 10^{-9} \; \mathrm{s}\]

Step 5: Interpret the Result

The time it takes for light from the strobe to reach the mechanic's eye is \(2.5 \times 10^{-9} \; \mathrm{s}\) or 2.5 nanoseconds.

Key Concepts

Distance Calculation

Determining the distance light travels is crucial when studying its behavior in physics. In this context, distance calculation is straightforward as the light travels directly from the strobe to the mechanic's eye.

To clarify, the distance in this problem is simply the distance from point to point, without any obstacles altering its path.

• The strobe light is held 0.20 meters from a flywheel, but this does not alter the direct path to the mechanic's eye.
• Therefore, the relevant distance to consider is 0.75 meters from the strobe to the eye.

This principle of assuming a linear path is standard in many basic physics calculations involving light in a straight line. Keeping calculations simple by focusing directly on the path from the source to the point of observation helps in various applications, including engineering and applied sciences.

Light Travel Time

Understanding how long it takes light to travel between two points can be intriguing! Light travel time calculations involve both the distance light must travel and its speed.

• Light speed in air is approximately \(3 \times 10^8\; \mathrm{m/s}\).
• Using the direct distance of 0.75 meters calculated earlier, we can find the time using \( t = \frac{d}{v}\).

Substituting known values into the formula gives us: \[ t = \frac{0.75}{3 \times 10^8} = 2.5 \times 10^{-9} \; \mathrm{s} \]This result, 2.5 nanoseconds, shows the incredibly short time it takes for light to travel even a relatively small distance! Light's speed means that over everyday distances, this time is almost instantaneously small. This is part of why light is so essential in everything from communications to cars.

Applied Physics

Physics principles, such as the speed of light, play a vital role in applied physics, showing their relevance to real-world scenarios like timing engine movements. This problem gives insight into just one small application of these principles.

• Mechanics often use tools like strobe lights to make precise measurements and adjustments to engines, capitalizing on light's predictable behavior.
• With the knowledge that light takes 2.5 nanoseconds to travel 0.75 meters, mechanics can synchronize timing systems accurately.

These principles underscore how theoretical physics cross over into practical technologies, enhancing efficiency and accuracy in engineering. With an understanding of simple physics concepts, significant improvements and precise operations are easier to achieve, making physics a cornerstone of technological advancement.