To build the pyramids in Egypt, it is believed that giant caus...

Question

To build the pyramids in Egypt, it is believed that giant causeways were constructed to transport the building materials to the site. One such causeway is said to have been 3000 ft long, with a slope of about 2.3°. How much force would be required to hold a 60-ton monolith on this causeway?

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Accepted Answer

Hey, everyone. Here we are given a cylindrical container filled with chemicals is being transported on a conveyor in a factory. A segment of the conveyor has a length of 30 ft and is inclined at an angle of 9.2 degrees with the horizontal. If the container weighs £173 what force is required to hold it as it passes through the incline segment? We have four answer choice options. A £29.8 B £24.3 C £31.6 and D £27.7. To begin this problem, we just need to create a sketch containing our given information. So to start the sketch, we need to draw our horizontal line. And from there, we can sketch the inclined segment of the conveyor by just drawing a line which extends upward from the horizontal. And we know that the angle in between the incline segment and the horizontal is given as 9.2 degrees. So we can go ahead and label that angle next, we can represent our cylindrical container on the incline segment as just a vertical rectangle. And so now we are also given that the container weighs £173. So this tells us we have a weight force which we need to illustrate on our sketch as just an arrow which extends from the container directly downward so that it is perpendicular to the horizontal. And now we just want to label this arrow as £173. And again, we were asked to find the force required to hold our container on the incline segment. So we want to represent this unknown force as an arrow which extends from the container upwards along the ramp. And now we just want to label this arrow as our unknown force. F. And with this, we have sketched all of our given information. So now we just want to continue adding to this sketch so that we find enough information to solve four F. So first, we just want to extend a line downward from our ramp or our inclined conveyor down to the horizontal so that the line is perpendicular to the horizontal. And with this, we have formed a right triangle underneath our container. However, this triangle alone doesn't give us enough information to solve for F. So instead we want to recreate this triangle utilizing our weight force. So first, we just want to extend another line downward from our container, except this line needs to be perpendicular with the inclined segment. And so now we have one line perpendicular to the ramp and the other line, the arrow, our weight force perpendicular with the horizontal. So this tells us that the angle in between these two lines is our 9.2 degrees angle. And now to complete this triangle, we want to recall our unknown force f as it is parallel to the ramp or our inclined segment. And so we know that this forms a 90 degree angle with our newly added line. So we just want to rewrite this force by just drawing an arrow from our new line to the weight force. And we know this now forms our 90 degree angle. And we just want to label this side of the triangle as our unknown force F. And with this new triangle, we see we have one angle known as well as the length or value of the hypotenuse. And so we have enough information to solve four F. So first, we just want to recall that sine of theta is equivalent to the opposite side from the angle divided by the hypotenuse. So now using our new triangle, we know that sine of 9.2 degrees is equivalent to F divided by £173. And now with our equation here, we just want to solve it for F by first multiplying both sides by the right hand side's denominator. So we multiply both sides by £173. And now just rewriting, we find that F is equal to £173 multiplied by sine of 9.2 degrees. And now just evaluating this expression, we find that F is equal to £27.6594. And so now we just want to round this value to the nearest 10th. And so we find that F is approximately equal to £27.7. And with this final rounded answer, we are left with answer choice D where again, we found that our unknown force is £27.7. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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