A 1125-kg car and a 2250-kg pickup truck approach a curve on a highway that has a radius of 225 m. (a) At what angle should the highway engineer bank this curve so that vehicles traveling at 65.0 mi/h can safely round it regardless of the condition of their tires? Should the heavy truck go slower than the lighter car?

Video transcript

Welcome back everybody. We have two vehicles that are running along this track right here and they are approaching some sort of banked curve. Now, these two vehicles are going to be 1000 kg van which I represent with this rectangle and a 2000 kg bus which I represent with this one. Now we are told a couple different things about this track and these vehicles as well. We're told that the mass of our van Is equal to 1000 kg. We are told that the mass of our bus is twice as much. Now. We are also told that the radius of curvature for the track is 200 m and we are told that both vehicles are approaching at a velocity of 40 m/s. Now approaching this banked curve, this curve from kind of the side view is going to look something like this and we are tasked with finding in part a what this banking angle data is going to be. Let's go ahead and tackle part A here. Well, We are told just by a formula here that the tangent of our banking angle is going to be equal to the velocity of the vehicles divided by the acceleration due to gravity times the radius of the circle. So let's go ahead and plug those values in. So we have that the speeds of the vehicles are 40, which we're going to square that divided by 9.8 times the radius of the track which is 200, which when you plug this into your calculator, you get 0.816. Now, I am going to take the arc tangent of both sides to isolate beta and we get that data is equal to 39.2 degrees. So now let's move on to part B. Here is the van or the bus going to be moving slower. It's it's should the bus move slower than the van is the way that they phrase it. Well, let's look at this formula again, right here, nowhere in this formula do we need to take into consideration the mass of the individual vehicles may Meaning that the mass is not taken into account and that these two vehicles should be traveling at the same exact speed. So if we're looking at the same speed with a banking angle of 39.2°, we get our final answer of a thank you guys so much for watching. Hope you all enjoyed the video. We will see you all in the next one.