Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

A man is dragging a trunk up the loading ramp of a mover's truck. The ramp has a slope angle of $20.0^{\circ},$ and the man pulls upward with a force $\vec{F}$ of magnitude 375 $\mathrm{N}$ whose direction makes an angle of $30.0^{\circ}$ with the ramp. (See Figure $4.34 . )$ Find the horizontal and vertical components of the force $\vec{\boldsymbol{F}}.$

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$F_{h}=241.05\mathrm{~N}$$F_{v}=287.27 \mathrm{~N}$

Physics 101 Mechanics

Chapter 4

Newton's Laws of Motion

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Cornell University

Hope College

University of Winnipeg

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

02:18

A man is dragging a trunk …

01:28

03:38

"A man is dragging a …

01:32

01:50

03:25

02:34

$\mathrm{A}$ man is draggi…

01:40

Find the magnitude of the …

02:54

Force A cart weighing 40 l…

01:43

A shipping crate that weig…

03:52

Tow forces: A large van ha…

Okay, guys. So, um, our problem here we are, given that a blocks being pulled up a ramp which sits at an elevation of 20 degrees above the horizontal by a force that is 30 degrees above the ramp, as seen in my little diagram here. Okay, so the ramp is at 20 degrees above the horizontal and the forces 30 degrees above that ramp, so well, we can really do here is combine these two angles and say the forces really just directed at a direction of 50 degrees above the horizontal okay, were also given that that force has a magnitude 375 Newton's. And then we're asked to find f sub X and F sub y or the horizontal and vertical components of the force, respectively. Okay. Our key equations we're gonna be using here are that the magnitude of a vector F is going to be equal to the sum of its X and Y components of subjects in f sub y. And in this particular case, as in most cases, F sub X will be equal to F coast on data in the exact direction and have some why will be equal to f A sign theater in the Wyatt Direction. Now, how do we achieve these two expressions here? Cause they can change depending on the situation. So let's take a look at that on this tab here, or have shown how to get that more clearly. So if you will look over here, I've re drawn our triangle. This is simply the fourth diagram that I drew here, but in a little bit more detail. So our forces directed this way at 50 degrees over the horizontal, and our X component of the force will be directed along the X axis running this way. Ah, why component of the four could be running vertically this way. Okay. And so we're going to use our old trig rules here to find what each of these components will be. So we lay without a triangle like this, right? Triangle. We have our angle fade in the bottom here. Then we have the adjacent leg, the opposite leg in the iPod news. Okay, so we know that co sign theta is equal to the adjacent leg over the high pod news. So, in the context of our problem here, that's gonna mean that CO sign of 50. It's going to be equal to the adjacent leg R F sub x over the magnitude of the force, which is the I pod news. Okay, so now, as I've shown with this arrow here, we can simply multiply the iPod news or if over to the other side of the coastline of data. And that's how we get F sub X is equal to f coast on data here. Same story for the y directional force. Okay, so sign if data is gonna be equal to the opposite over the high partners in this case, we can multiply ha partners over again. Which, of course, is F. As you will remember, I as sub y is going to be equal to f sign of Dana. Okay, so that's how we got those two relations in the equations I gave in the beginning of the video. So now it's simply a matter of plugging in our known values and, um, calculating our results. So have setbacks will be equal to 375. The bag to the fourth time's the coast sine of the angle, which is 50. Give us f sub x 241.5 Newton's s. So why Now we do 375 for the magnitude does the sign of 50 degrees gives us 287.27 Newton's now the units for both of these guys should be Newton's, as they're both forces. And the initial force was given in Newton's. So that is how we break this force down into the horizontal. We're in a cheerful horizontal and vertical components. Okay, this is a, ah pretty important tool and most of physics. Ah, you're gonna use it a lot, especially when you're working with forces and, um, basic mechanics problems like this. So it's really an important concept to get. And really, it's not a physics concept, perceive as it is more of a math, trigonometry and vector, um, idea. So if you don't understand this, make sure you have plenty of practice and do understand it if you want to be successful. And one more thing. If you didn't get the right answer for either of these, you may want to check and make sure that your calculator is set to degrees mode and our radiance about as we were using 50 degrees in this case. Um, so thanks, guys. Let me know if you have any questions and have a good day.

View More Answers From This Book

Find Another Textbook

Numerade Educator