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Numerade Educator

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Problem 5 Medium Difficulty

A barge of mass $5.0 \times 10^{4} \mathrm{kg}$ is pulled along the Erie Canal by two mules, walking along towpaths parallel to the canal on either side of it. The ropes harnessed to the mules make angles of $45^{\circ}$ to the canal. Each mule is pulling on its rope with a force of $1.0 \mathrm{kN} .$ How much work is done on the barge by both of these mules together as they pull the barge $150 \mathrm{m}$ along the canal?
CAN'T COPY THE FIGURE

Answer

$2.1 \times 10^5 \text{ J}$

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Video Transcript

this question asks us to calculate the work done by two mules as they pull a barge up a canal. Part of the challenge of this question is drawing out and accurately capturing all the information that is presented in the problem in a way that's gonna make it easier for us to actually do this calculation. So that's why let's walk through that process together. So the question tells us that two mules air pulling the barge that I've already drawn right here down this canal to the right is how in a draught. So let's draw these mules on here. They're going to be little circles because there's no way I can accurately draw a barge. I mean, a mule, and they're pulling it like this. Now the question also tells us that the ropes that the mules are pulling with makes an angle of 45 degrees with the canal. It also tells us that each mule is pulling with a force of 1.0 killing Newtons, which I'm gonna immediately right in standard notation without the kill Indians there. It's that I don't forget about that when I'm plugging it into my formula at the end. It also tells us that the barge moves 100 and 50 meters upstream and were also given the mass of the barge, which is 5.0 times 10 to the four kilograms. Now the question is asking us to solve for the work. So the formula we have here is that work equals force times Displacement times co Sign of theta where theta is the angle between the force and the displacement. So going back to our diagram here, our displacement of the barge is moving directly to the right. Our forces are each pulling at 45 degree angles. Two the displacement. So when I'm calculating the work, the angle between each force that I'm gonna use is 45 degrees. So let's go ahead and plug all this information in. So I'm gonna slap a two out front here because we have two mules, each applying an identical force. So I'm just gonna calculate the work done by one. And then this factor of two is gonna double it because there's two mules. The force each meal is using is 1000 Newtons. The displacement of the barge overall is 100 50 meters and then the coastline of the angle between the force and the displacement, luckily for us is the same for each one. It's gonna be co sign 45. So doing some math here, the we've got 2000 times 150 which is basically 300 1000. And then the coastline of 45. You can either plugged that into a calculator or, if you haven't memories that it's rude to over to. Either way is gonna work for you. Either way, plug that into calculator to get a numeric answer, and we get something along the lines of 21213 to duck That that Jules as her answer. So rounding this to the appropriate number of significant digits and writing it in scientific notation each of our numbers, given the problem, was written with two significant digits. So I'm gonna take the 2.1 and write that as times 10 to the five jewels as the work done on the barge by boat