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Chapter 6: Problem 44

A locomotive does \(7.9 \times 10^{11} \mathrm{J}\) of work in pulling a \(3.4 \times 10^{6}-\mathrm{kg}\) train \(180 \mathrm{km} .\) Find the average force in the coupling between the locomotive and the rest of the train.

Short Answer

Expert verified
The average force in the coupling between the locomotive and the rest of the train is approximately 4394444 N

Step by step solution

01

Understand the Problem

We're given the work done by the locomotive (\(7.9 \times 10^{11} \mathrm{J}\)) and the distance the train has been pulled (\(180 \mathrm{km}\)). We are asked to find the average force in the coupling, which according to the work-done principle, can be found from the formula \(F = \frac{W}{d}\). Therefore, to get the force in the coupling, we need to divide the work done by the distance.
02

Convert kilometres to metres

The distance travelled is given in kilometres. The standard unit of distance in physics is the meter. Therefore, we need to first convert kilometres into metres by multiplying by 1000. Hence, \(180 \mathrm{km} = 180000 \mathrm{m}\).
03

Calculate the Force

Now, we substitute the values we have into the rearranged formula to calculate the force. This gives \(F = \frac{7.9 \times 10^{11} \mathrm{J}}{180000 \mathrm{m}}\). Simplifying this expression will yield the force.

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