![]() I would really appreciate any help, even if it's just pointing me in the right direction as far as which equation to use, I'm not necessarily asking anyone to work it out. But if it helps ya verify results, here are the answers: Not sure which angular motion/centripetal force equations to use. I actually have the answers to the problem, but of course it doesn't help me understand the problem nor the process in getting there. Express your answer in terms of the pilot's weight mg. If the speed of the aircraft is 700 km/h and the radius of the circle is 2.0 km, calculate the normal forces exerted on the seat by the pilot at the bottom and top of the loop. In order to still be moving in a circle of radius R, the lowest speed would have no normal force pushing on you.A jet pilot puts an aircraft with a constant speed into a vertical circular loop. Thus you will need to know the angle, or where you are in the loop as a function of time. This means you wouldn't be moving in a circle. Me2 - consider that centripetal force resolved in the vertical axis will counteract the normal gravitational force thus lessening normal force which will be minimum at the top of the loop (considering forward velocity constant around a circular loop). ![]() If you just barely make it to the top, you will be there with a speed of zero. Making it to the top and making it around the loop are two different things. What does this say? This says that if the coefficient of friction is less than around 0.18, you will make it to the top. With the parameters as they are, what is the maximum value of the coefficient of friction for which you can get over the loop? Here is a plot of the maximum height in the loop for different starting values of μ. Any faster and you might die from the massive acceleration. If you are going any slower, you wouldn't make it over the loop. With a radius of 3 meters, this gives an acceleration of 10.2 g's. If the slider is at the bottom of the loop going 16 m/s, then the following must be true for the forces in the y-direction (at that instant): Just the normal force would be easy to calculate. 10 g's when the slider first enters the loop? That seems crazy high. Instead, the slider would fall and crash into the top of the tube at a lower point. This means that in order to stay on that circle, the tube would have to pull on the person. Second, in the case where the slider goes back down the direction of the normal force changed. Notice two things about the normal force (white vector). Oh, you might notice that my animation included vectors representing the three forces. If I change the coefficient of kinetic friction to 0.1, then the speed entering the loop would be 16.5 m/s and the slider would make it over the top. There is that water sliding down with you after all. ![]() I guess my value for the coefficient of friction was too high. Good thing they put that escape hatch in the tube. In this case the slider didn't make it around the top of the loop. Why? Here is a quick animation of the loop if the starting speed is 15 m/s. This would put the speed entering the loop at 15 m/s (33.5 mph). If I assume a loop diameter of 20 feet (6.1 meters), a measurement of the image shows the starting height would be about 16.2 meters above the bottom of the loop. The first question that comes to my mind: what kind of forces would you feel if you make it around the loop? Ok, I first need to determine the starting height. From here, I can use the usual numerical model. But the point is that now I know all three vector forces (gravity, friction, and the normal force). Here the "v-hat" is a unit vector in the direction of the velocity. With the normal force, I can then find the friction force. The direction of this normal force will be towards the center of the circle. ![]() Since I know the acceleration in the radial direction and the gravitational force, I can solve for the unknown normal force. This radial acceleration is due to two forces: the normal force (which is in the same direction as the radial acceleration) and a component of the gravitational force. From this I can calculate the acceleration in the direction towards the center of the circle based on the velocity and the radius. First, I will assume the trajectory is in the path of a circle. However, the normal force doesn't depend on these things. G forces in loops: CALCULATION OF THE GS FELT in a loop: Use this circular motion formula: Where v is the velocity of the marble and R is the radius of. This method works well if I can find the forces based on position (like a spring) or velocity (like air resistance). Use the momentum to find the change in position. ![]() Use the total force to determine the change in momentum and thus the new momentum.The main process in these numerical calculations is to do the following: But then how do we deal with this force? A simple numerical model won't work. ![]()
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