A force of 30.0 lb is required to hold an 80.0-lb pressure was...

Question

A force of 30.0 lb is required to hold an 80.0-lb pressure washer on an incline. What angle does the incline make with the horizontal?

Accepted Answer

Hey, everyone here we are given Robert takes out his baby for an evening walk. The baby is sitting on a tricycle. Robert is holding a £100 baby cycle with a force of £50 outside the ramp of his house. Find the angle of inclination of the ramp with the ground. We have four answer choice options. A 30 degrees B 25 degrees C 35 degrees and D 25 degrees. So to begin this problem, we need to start by creating a sketch containing our given information. So to start this sketch, we just want to draw a horizontal line to represent the ground. Now, we need to draw in our ramp. So we just need to add another line coming upwards from the ground at some angle. And now we want to label the angle in between the ground and the ramp as angle theta and this is the angle we will be trying to find. And now we can represent the tricycle as just a rectangle on our ramp. And now we are told that the tricycle experiences a force of £50. So we just want to illustrate this force as an arrow going from our rectangle upwards along the ramp. And now we just need to label this arrow as £50. Next, we are told that the tricycle weighs £100. So we have our weight force, which we also need to add. And so we just need to draw another arrow going from the rectangle directly downwards and this arrow must be perpendicular to the ground. And so we will label this arrow as the £100 force. And now that we have finished sketching all of our given information, we want to begin finding our value for theta. So first, we just want to complete the triangle that we have underneath our rectangle. So we just need to draw a line coming down from the ramp to the ground and this line must be perpendicular to the ground. Therefore, we get our 90 degree angle and we complete our right triangle. However, looking at this triangle, we can notice that we do not have any of our sides identified. So we have no way to find the value for theta. So we need to recreate this right triangle utilizing our weight force. And so to do this, we just need to draw another line going from the rectangle downwards except this line must be perpendicular to the ramp. And so now, since we have this line perpendicular to the ramp, and we have our weight force perpendicular to the ground, this tells us that the angle in between these two lines is our angle, theta. And now to complete our triangle again, we have our line perpendicular to the ramp. And we also have our £50 force which is parallel to the ramp. So we know that the line and our £50 force form a 90 degree angle. So just drawing an arrow from the line to our weight force, so that the heads of both arrows are touching, we form our 90 degree angle and we just need to label this arrow as £50. So now we have finished our new right triangle and we can notice we have two sides identified or rather the hypotenuse and one length. And so now we can easily find our value for data by recalling that sign is equal to opposite the opposite side divided by the hypotenuse. And so using this information and the information from our new triangle, we find that sign of theta is equivalent to the opposite side, which is £50 divided by the hypotenuse, which is £100. Now, we just need to solve for theta by first simplifying the right hand side. So here we can notice that the pound units cancel each other out. And we can also simplify 50 divided by 150 divided by 100 simplifies to one half. So so far, we have sin of theta is equal to one half. And now just solving for theta, we need to take the sine inverse of both sides. And so we have theta is equal to sine inverse of one half. And now just evaluating this expression s inverse of one half gives us 30 degrees. Therefore, we have found that theta is equal to 30 degrees. This leaves us with answer choice. A where again, we found that the angle in between the ramp and the ground is 30 degrees. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

A force of 30.0 lb is required to hold an 80.0-lb pressure washer on an incline. What angle does the incline make with the horizontal?

Key Concepts

Resolving Forces on an Incline

Trigonometric Ratios (Sine, Cosine, Tangent)

Equilibrium of Forces

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