Question

Part II - Is It Even Possible? One way that mathematical models are used by scientists and engineers is to make predictions about how a system will behave. In the video, the engineers use a simple kinematics model to predict how much the glider would need to accelerate as it is pulled along the runway in order to launch. Based on the aerodynamics of the glider, the engineers calculated it would need to reach a speed of 40 mph to successfully launch into the air. The roof is 160 feet above the ground, and the runway (built from tables on top of the peak of the roof) was about 60 feet long. The first question the engineers need to figure out is if it is theoretically possible to reach the desired launch speed given the length of the runway and the height of the tower. Questions 1. Given this information, what must the acceleration of the glider be to reach the launch velocity by the end of the runway? (Convert all values to SI units.) 2. The engineer wants the glider to accelerate at a rate of 1.2g (11.6 m/s). How does this compare to your result? Why would the engineer over-estimate the acceleration?

Answer 1

modification in system as in 2nd figure in question will be able to generate accleration 1.29. wood H 131 12 FBD OK Tub Hub 62 Total String length = litt2 tls. = const & L2=63 Wtub lang Awood = -2x ditub

so to get a wood = 1129 Atüb= 0.69 By choosing sufficient higher weight tub, we can get accelaration 1.05 0.6g. © Scaled down model help us to understand approximate results of real case scenario with very low investment and faster, so that before implementing the actual system, we can have some good probability of working of system. Benifit of this system is : that it saves cost bigger modificato in actual system. Limitation of this model is that : we cannot test all the parameters that actual system may face during its working

Taunch speed = 40 mph = 17.8816 m/s Tength of Runway = 60 feet = 18.288m - By Mewton's 3rd equation of motion, v2=42+2 as 17.88162 = 02 + 2x ax 18.288 accelaration Required à = 8.74211 m/s2 Now engineer wants q=1:29 a=11.6m/s2 this accelaration is higher than the theorotically required acceleration

Engineer would have overestimated the accelaration in order to compensate factors like air. diag for glider, kriction, weight and inertia effect of system. Also this model is theorotical.so in order to consider practical things, like non uniformity in acceleration itselt, engineer would have over estimated accelaration to 11.6m/52 Simply using bath tub will inot. generate accleration of 1.29 as maximum accleration that bathtub will have under gravity force will be less than g.. and in ideal condition, it of Can be maximum equal to g.
​​​​​​in the solution, when acceleration of wooden block is calculated, length of string is constant but Length l1, l2 and l3 changes as bathtub moves downwards. Change in length l1 corresponds to displacement of wooden block. And similarly change in length l2 corresponds to displacement of tub.