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Chapter 16: Problem 2

Consider the freight train in Figure \(16.6 .\) Suppose that 15 boxcars pass by in a time of 12.0 s and each has a length of \(14.0 \mathrm{m}\). (a) What is the frequency at which each boxcar passes? (b) What is the speed of the train?

Short Answer

Expert verified
(a) 1.25 boxcars/s, (b) 17.5 m/s

Step by step solution

01

Calculate the Frequency of Boxcars Passing

Frequency, by definition, is the rate at which something occurs over a particular period of time. It's calculated as the number of events divided by the time taken for these events. Here, the event is each boxcar passing by. We have 15 boxcars passing in 12.0 seconds. Hence, the frequency \( f \) can be calculated using the formula:\[ f = \frac{\text{Number of Boxcars}}{\text{Time}} = \frac{15}{12.0} = 1.25 \text{ boxcars per second} \]
02

Calculate the Speed of the Train

The speed of the train is the distance it covers per unit of time. Since each boxcar is 14.0 meters long, the entire length of 15 boxcars is:\[ \text{Total Distance} = 15 \times 14.0 = 210.0 \text{ meters} \]The speed \( v \) of the train can be calculated using the formula:\[ v = \frac{\text{Total Distance}}{\text{Time}} = \frac{210.0}{12.0} = 17.5 \text{ m/s} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Speed Calculation
In physics, speed is a measure of how fast an object is moving over a certain period of time. It tells us how much distance the object covers in a specific time interval. Let's simplify speed into two components: distance and time. To calculate speed, you use the formula:\[ v = \frac{\text{Total Distance}}{\text{Time}} \]For example, if a train travels 210 meters in 12 seconds, its speed would be \( 17.5 \text{ m/s} \). This means every second, the train moves 17.5 meters. Knowing how to calculate speed helps us understand the dynamics of moving objects, making it easier to predict when they'll arrive at a destination.
Rate of Events
The term 'rate of events' refers to how frequently a certain event repeats over a specific period. It's a handy way of figuring out patterns and predicting future occurrences. In the case of the freight train, we calculated the rate at which boxcars pass using the concept of frequency.The formula used is:\[ f = \frac{\text{Number of Events}}{\text{Time}} \]By identifying the number of boxcars that pass in a given time (15 boxcars in 12 seconds), we find the frequency to be \( 1.25 \text{ boxcars per second} \). This tells us that, on average, a bit more than one boxcar passes every second. Having a grasp on the rate of events can be incredibly useful for scheduling and planning.
Distance Calculation
Understanding how to calculate distance is crucial, especially in tasks involving movement or travel. Distance signifies the total path an object travels, and sometimes you might be given the distance in segments, like the length of individual boxcars in a train.If you know the number of segments and their individual lengths, you can calculate the total distance by multiplying:\[ \text{Total Distance} = \text{Number of Segments} \times \text{Length of Each Segment} \]For instance, if each boxcar is 14 meters long, and there are 15 boxcars, the total distance the boxcars span together on the train is 210 meters. Knowing how to calculate distance helps in understanding how far something has traveled, which is essential for determining both speed and planning routes.

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Most popular questions from this chapter

An ultrasonic ruler, such as the one discussed in Example 4 in Section \(16.6,\) displays the distance between the ruler and an object, such as a wall. The ruler sends out a pulse of ultrasonic sound and measures the time it takes for the pulse to reflect from the object and return. The ruler uses this time, along with a preset value for the speed of sound in air, to determine the distance. Suppose that you use this ruler under water, rather than in air. The actual distance from the ultrasonic ruler to an object is \(25.0 \mathrm{m}\). The adiabatic bulk modulus and density of seawater are \(B_{a d}=2.37 \times 10^{\circ} \mathrm{Pa}\) and \(\rho=1025 \mathrm{kg}\) \(\mathrm{m}^{3},\) respectively. Assume that the ruler uses a preset value of \(343 \mathrm{m} / \mathrm{s}\) for the speed of sound in air. Determine the distance reading that the ruler displays.

A wire is stretched between two posts. Another wire is stretched between two posts that are twice as far apart. The tension in the wires is the same, and they have the same mass. A transverse wave travels on the shorter wire with a speed of \(240 \mathrm{m} / \mathrm{s} .\) What would be the speed of the wave on the longer wire?

A hunter is standing on flat ground between two vertical cliffs that are directly opposite one another. He is closer to one cliff than to the other. He fires a gun and, after a while, hears three echoes. The second echo arrives \(1.6 \mathrm{s}\) after the first, and the third echo arrives \(1.1 \mathrm{s}\) after the second. Assuming that the speed of sound is \(343 \mathrm{m} / \mathrm{s}\) and that there are no reflections of sound from the ground, find the distance between the cliffs.

A Mysterious Underwater Object. You and your team are on a reconnaissance mission in a submarine exploring a mysterious object in the cold waters of the Weddell Sea, off the coast of Antarctica. The sonar indicates that the object, which had otherwise been moving erratically, has changed course and is now on a direct collision course with your sub. The captain issues an "all stop" order, bringing the sub to a halt relative to the water. The sonar operator "pings" the object, which amounts to sending a short blast of sound in the direction of the object. The emitted sound wave has a frequency of \(1550 \mathrm{Hz}\) and a speed of \(1552 \mathrm{m} / \mathrm{s}\) (the speed of sound in seawater). The sound reflects from the object and returns \(2.582 \mathrm{s}\) after it was emitted from your sub, and its frequency has shifted to \(1598 \mathrm{Hz}\). (a) How far from the sub was the object when the sound reflected from it? (b) What is the object's speed? (c) How long after you receive the return signal will it take the object to reach your submarine?

Tsunamis are fast-moving waves often generated by underwater earthquakes. In the deep ocean their amplitude is barely noticeable, but upon reaching shore, they can rise up to the astonishing height of a six-story building. One tsunami, generated off the Aleutian islands in Alaska, had a wavelength of \(750 \mathrm{km}\) and traveled a distance of \(3700 \mathrm{km}\) in \(5.3 \mathrm{h}\). (a) What was the speed (in \(\mathrm{m} / \mathrm{s}\) ) of the wave? For reference, the speed of a 747 jetliner is about \(250 \mathrm{m} / \mathrm{s}\). Find the wave's (b) frequency and (c) period.
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