Kami is walking through the airport with her two-wheeled suitcase. The suitcase handle is tilted 40° from vertical, and Kami pulls parallel to the handle with a force of 120 N. (Force is measured in newtons, abbreviated N.) What are the horizontal and vertical components of her applied force?

Video transcript

Hi, everyone in this particular practice problem, we are asked to calculate the FX and F Y components or the X and the Y components of the applied force. When a fridge is being pushed on a horizontal floor with a forced f of magnitude 85 Newton making an angle of degrees with respect to the vertical axis. The force obviously is going to be projected along the X and the Y axis. And we're asked to find the magnitude of the FX and the F Y components of that force. So first of all, we want to do is to draw a diagram of our system to make it easier for us to visualize our projection. So first, we have a fridge which I'm going to indicate with this um square right here and the fridge itself will actually have or we will have a horizontal and vertical axis for the projection. And as it is written in our problem statement, we will have a force with uh 35° uh Angle from the vertical axis. So this force right here is 85 Newton and this angle right here. uh I'm just gonna call it with the Is going to be 35 degrees just like some. So as always, we will have a Y and an X component of the projection. And the Y component is going to be F Y and the X component here is going to be FX on the horizontal axis. So it says X axis and this is going to be R Y axis just like soap. And now we are pretty much ready to actually determine the FX and the F Y component. So the fourth factor F, the four vector F will have a horizontal component FX in the I factor notation and a vertical component F Y in the J factor notation using the trigonometric ratio where we will have a right angle formed by the factors FX F Y and F which I'm going to show in this figure right here, right angle where we will have an F and F Y add an FX here. We can actually use this trigonometric creation to determine our values. So first using this um triangle right here with the data being here from the uh vertical axis, then cosine of Phi or cosine of theta is going to be equals two. We want to recall that adjacent over the hypothesis and that will be F Y over the hypotenuse over here which is going to be F just like. So, so this is going the cosine of phi is going to be F Y over F next, we'll have, we will use sign of five, we will be, which will be opposite over the hypotenuse, which will be FX over F, opposite over the hypotenuse. So rearranging this, we can actually find F Y to be F multiplied by cosine of theta and FX to be equals to F multiplied by sign of theta. We know what the F is, we know what the theta is. So we can calculate this, we can substitute all the known values. And F Y will then be F, which is 85 Newton multiplied by cosine of degrees. And this will give us an F Y value Of 9 uh 69.6 Newton, 69.6 Newton. And that's the F Y. The same goes with the FX FX equal to F multiplied by sine of theta, which will be 85 Newton for the F multiplied by sine of 35 degrees for the theta. And that will give us an FX value of 48.8 Newton. So the FX component is going to be 48.8 Newton and the FY component is going to be 69.6 Newton when a force is being applied with a magnitude of 85 Newton making an angle of 35 degrees with respect to the vertical axis. And that will give us the answer to B option A with an FX of 48.8 Newton and F Y of 69.6 Newton. So option A is going to be the answer to this practice problem and that will be all for this video. If you guys have any sort of confusion, please make sure to check out our other lesson videos on similar topics and that'll be all for this one. Thank you.