A man is dragging a trunk up the loading ramp of a mover's truck. The ramp has a slope angle of 20.0°, and the man pulls upward with a force F→ whose direction makes an angle of 30.0° with the ramp (Fig. E4.4). (b) How large will the component Fy perpendicular to the ramp be then?

Video transcript

Hey, everyone in this problem, we're told that ramps are useful when loading trucks. So we have a situation where a worker is going to pull a trolley being loaded on a truck with an upward force F that has a direction of 28 degrees with the ramp. The rank has a slope angle of 15 degrees. What is the value of the component F Y perpendicular to the ramp? When the FX component parallel to the ramp is equal to nudes. We're showing a diagram. We have our ramp which makes an angle of 15 degrees with the ground on top of that ramp, we have our trolley and we have our worker who's pulling that trolley and they're pulling that trolley at an angle of 28 degrees with respect to the ramp up to the truck. We have four answer choices here all in Newton's option. A 40.3, option B 75.9, option C 45.7 and option D 162. Now, we're given a lot of information here. It seems like a complicated question, but let's just break out what we're trying to find OK. What we're trying to find is the Y component of the force F. OK. So I'm gonna take this force F and I'm gonna write it on the right hand side here and I'm just gonna tilt it so it's going straight. We have our force F and we know that the angle to the horizontal is 28 degrees. OK? In the case where it's actually on the trolley, that angle is to that rape and that angle is 28 degrees. What we want to find is this force F Y, the Y component of the force, right? And we're told that the X component of the force his 86th new. If you look at this, what you'll notice is that we have one side of our triangle and we know the angle that's enough to find this F Y. And because we have a 90 degree angle here. So all we need to do here is do some triangle math. So we have the, the tangent of our angle 28 degrees. It's gonna be equal to the opposite side which is F Y divided by the adjacent side, which is 86 newtons. We're gonna multiply both sides by 86 newtons. We get that F Y is equal to tangent with 28 degrees multiplied by 86 newtons, which gives us a Y component of this force of 45. newtons. So again, we were given a lot of information. But all we needed to do here was break down that force into its components using some triangle math. We're gonna round to one decimal place like the answer choices. And we see that the Y component of the force F Y is gonna be C 45.7 newtons. Thanks everyone for watching. I hope this video helped see you in the next one.