Problem 3 - University Physics with Modern Physics

Question

How many nanoseconds does it take light to travel 1.00 \(\mathrm{ft}\) in vacuum? (This result is a useful quantity to remember.)

Step-by-Step Solution

Answer

It takes approximately 1.0167 nanoseconds for light to travel 1 foot in a vacuum.

Step 1: Understanding the Speed of Light

The speed of light in a vacuum is a constant and denoted by the symbol \( c \). Its value is approximately \( c = 299,792,458 \) meters per second.

Step 2: Convert Feet to Meters

We need to convert the distance from feet to meters. Since 1 foot is equal to 0.3048 meters, we have: \( 1 \text{ ft} = 0.3048 \text{ m} \).

Step 3: Calculate the Time in Seconds

Time can be calculated using the formula \( \text{time} = \frac{\text{distance}}{\text{speed}} \). Substituting the values, we get: \[ \text{time} = \frac{0.3048 \text{ m}}{299,792,458 \text{ m/s}} \].

Step 4: Calculate the Time in Seconds

Perform the division to find the time in seconds: \[ \text{time} \approx 1.0167 \times 10^{-9} \text{ s} \].

Step 5: Convert Seconds to Nanoseconds

Since 1 nanosecond (ns) equals \( 10^{-9} \) seconds, we convert the time from seconds to nanoseconds: \[ 1.0167 \text{ ns} \].

Key Concepts

Physics Problem Solving

Solving physics problems involves breaking down a situation into manageable parts. This problem is about finding the time it takes for light to travel a certain distance. By understanding the constant nature of the speed of light in a vacuum, we can apply relevant formulas to calculate the desired result. Light travels incredibly fast, so it is important to use precise and systematic approaches when solving related problems.
To master this, you need to:

• Comprehend the constants involved, like the speed of light (denoted as \(c\) and approximately equal to \(299,792,458\) meters per second).
• Identify what is asked, in this case, the time it takes for light to traverse one foot in a vacuum.
• Follow a systematic approach to apply mathematical and physics concepts, ensuring accuracy at each step.

By focusing on these aspects, solving such problems becomes less daunting, allowing you to handle more complex scenarios with confidence.

Unit Conversion

Unit conversion is crucial when dealing with physics problems, especially when dealing with international and local measurement standards. In this exercise, our goal was to determine how long it takes light to travel a specified distance. The initial distance was given in feet but needed to be in meters, since scientific calculations typically utilize the metric system.
To perform the conversion:

• Understand the conversion factor: 1 foot equals 0.3048 meters.
• Apply this factor to the distance in feet: \(1 \text{ ft} = 0.3048 \text{ m}\).

Accurate unit conversion ensures consistency in calculations and is often a deciding factor in problem-solving effectiveness. Developing a habit of verifying units and conversions is essential for aspiring physicists.

Time Calculation

Time calculation is a key element in finding out how long a process or event lasts. In our exercise, we used a formula to determine the time light takes to travel a given distance.The formula used is the fundamental equation: \[ \text{time} = \frac{\text{distance}}{\text{speed}} \]This involves dividing the distance (converted to meters) by the speed of light (\(299,792,458 \text{ m/s}\)). This results in the time in seconds: \[ \text{time} \approx 1.0167 \times 10^{-9} \text{ s} \]As it's evident, light travels very short distances in tiny fractions of a second.
By understanding this approach, you can tackle a variety of physics-based time problems, ranging from astronomical calculations to everyday time assessments.

Speed in Vacuum

The speed of light in a vacuum is a fundamental constant in physics. Denoted by \(c\), it is approximately \(299,792,458\) meters per second, an incredibly high speed that plays a critical role in the theories of relativity and quantum physics. In vacuum, light travels without interacting with matter, experiencing no resistance that could alter its velocity. This consistency makes it a reliable basis for scientific laws and equations.

• Understanding this constant allows for accurate predictions and measurements in various fields of science and technology.
• It serves as the ultimate speed limit in the universe, according to current physical theories.

By mastering the concept of the speed of light in a vacuum, you lay the groundwork for further exploration into the fascinating world of physics.