Question

2. (6 points) Daredevil Donny, an adventurous 8 year old kid, is setting up his latest death-defying stunt, which is shown below (not drawn to scale). He will be in

his wooden car (un powered, it just rolls down hills), starting on top of a ramp a height H above the road below. His car will roll down the hill, around a circular loop he's constructed, and then fly off a ramp, and over a school bus. To make it as exciting as possible, he wants it to look like he's not going to make it. So he wants to just barely have enough speed to make it around the loop,and then go flying off the ramp, and just barely clear the school bus (which, as everyone knows, is 4 meter stall). The loop he built has a radius of 5 meters. If he starts high enough (H) to just barely make it around without falling off, how far away from the ramp (L) should the back end of the bus be so that he just barely clears it? Assume that friction is negligible. a. You may notice that this looks fairly similar to the first problem in activity 35, except in that a ball was rolling down and around the loop instead of Daredevil Donny. There is another important distinction here though – I specified here that Donny "wants to just barely have enough speed to make it around the loop". In the problem in Activity 35, that wasn't a concern – and we ended up being able to completely ignore the loop.Just as with the Activity 35 problem, the loop won't change his speed (he’ll be coming out of the loop at the same speed he entered the loop, since there is no friction to take energy away) – but we need to figure out how fast he needs to be going to just barely make it around the loop. So, let's identify some important moments.Where he starts is clearly important, so let's call that moment A. We could then call the bottom of the hill our next moment, but that isn't necessary – we can use energy to go directly from moment A to the top of the loop.So let's call the top of the loop moment B. Then when he leaves the ramp will be moment C, and moment D will be when he just barely clears the back roof of the school bus. Label those above. b. We will first focus on moment B, to try to figure out how fast he has to be going to not fall off the loop. Draw a FBD of the car at the moment it is at the top of the loop (B). c. Hopefully you have a normal force in your FBD. If he’s going really fast, would that require a bigger or smaller normal force? If he's just barely making it around the loop, such that he is on the verge of falling off when he's at the top, what do you think that means about the normal force (if he is on the verge of falling off the loop)? d. Apply Newton's 2nd Law to the car at moment B. Notice that he is going in a circular path. In general, when we see something going in a circle, that is a tip-off that it might be worthwhile to apply Newton's 2nd Law to see if it tells us anything useful, since we know something about the acceleration of something going in a circular path. Your answer to part c hopefully tells you what to do with the normal force in your equation. Then solve for the speed (which should come into the equation from the acceleration being centripetal acceleration). e. Now you know how fast he has to be going to just barely make it around the loop. Now determine how high up (H) on the ramp he needs to start so that he will be going fast enough when he is at the top of the loop. This means using one of your "tools" to go from moment A to moment B. f. Now focus on the part where he leaves the ramp (moment C). You are presumably going to need to know how fast he's going there. Come up with a way of determining that speed (you could go from moment A to C or B to C). g. Now we need to figure out how far away the school bus should be (L in the picture). With projectile motion,that's going to generally still be done the same way we did at the beginning of the semester. See if you can figure out how to determine how far away the back edge of the school bus should be so that he barely clears it.(more room on the next page).

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