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You are working for the Highway Department. In mountainous regions, highways sometimes include a runaway truck ramp, and you are asked to help with the design of such a ramp. A runaway truck ramp is often a lane of gravel adjacent to a long downhill section of roadway where trucks with failing brakes may need assistance to stop. Working with your supervisor, you develop a worst-case scenario: a truck with a mass of 3.00 Ã— 10^4 kg enters a runaway truck lane traveling at 32.0 m/s. Experiments have shown that the coefficient of kinetic friction of truck tires moving through the gravel is 0.51. (a) Your supervisor asks you to advise her on the required length of a runaway truck lane on a section of ground next to the roadway that rises at a constant angle of 28.0Â°. (Give the minimum length of the roadway required in m.) (b) She also asks you to advise her on considerations to make about the runaway truck lanes if more massive trucks are approved and allowed to travel on this roadway. The more massive the truck, the longer the roadway required. The more massive the truck, the shorter the roadway required. The roadway required does not depend on the mass of the truck.

          
            You are working for the Highway Department. In mountainous regions, highways sometimes include a runaway truck ramp, and you are asked to help with the design of such a ramp. A runaway truck ramp is often a lane of gravel adjacent to a long downhill section of roadway where trucks with failing brakes may need assistance to stop. Working with your supervisor, you develop a worst-case scenario: a truck with a mass of 3.00 Ã— 10^4 kg enters a runaway truck lane traveling at 32.0 m/s. Experiments have shown that the coefficient of kinetic friction of truck tires moving through the gravel is 0.51. (a) Your supervisor asks you to advise her on the required length of a runaway truck lane on a section of ground next to the roadway that rises at a constant angle of 28.0Â°. (Give the minimum length of the roadway required in m.) (b) She also asks you to advise her on considerations to make about the runaway truck lanes if more massive trucks are approved and allowed to travel on this roadway.
The more massive the truck, the longer the roadway required.
The more massive the truck, the shorter the roadway required.
The roadway required does not depend on the mass of the truck.

Added by Mark H.

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00:01 Okay, so we're trying to design a truck lane and it's going to head up at 30 degrees.

00:06 And then we need to accommodate a truck of a certain mass with failed breaks at 110 kilometers per hour.

00:17 And then we want to know how long we should make the lane.

00:22 So let's go ahead and get down the givens of the problem, having some technical issues.

00:33 Okay, here we go.

00:33 So 30 degrees.

00:36 Let's go ahead and draw it.

00:40 And it's still going slow, but i think i'll just try to wait it out.

00:48 And the truck is going at a velocity 110 kilometers per hour.

01:00 Wow.

01:02 This seems big, but it might be confusing miles per hour.

01:20 Oops.

01:21 Let's see if i can undo that.

01:25 And the mass is 16 ,000.

01:30 I'm going to pause the video and let my computer load a bit.

01:35 Okay, i think it's good now.

01:37 So the mass is 16 ,000.

01:40 Let's go ahead and write that down, kilograms.

01:46 And so the idea is that this truck is going to kind of go up here and it's going to kind of slow its velocity down.

01:55 And we want to know what length we need to make it before the truck slows down.

02:05 So i remember seeing this first time in colorado.

02:09 Okay.

02:10 So, you know what? before i start the problem, i'd like to just convert everything to si if i anticipate that i'll have to do that.

02:17 So let's convert this hours to seconds.

02:20 So there's one hour.

02:28 So i want to multiply by one hour.

02:31 Per 3 ,600 seconds because there's 60 seconds in a minute, 60 minutes in an hour.

02:43 And so we can get the result in meters per second.

02:47 And so 110 times 10 for kilo kilo, 1, 2, 3, divided by 3, 3, plugging that into a calculator, i get 30 .6 meters per second.

03:08 Great, now that that is out of the way, let's kind of put this to the side and let's talk a bit about the physics of this problem.

03:15 So the idea is this goes up, it's course going to turn its kinetic energy into potential energy...