### Roller Coaster Design ProblemYou have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up an 11-meter-high hill, then descends 18 meters to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.0 meters and that a loaded car will have a maximum mass of 410 kg. For safety reasons, the spring constant should be 11% larger than the minimum needed for the car to just make it over the top.---#### Part A**Question:** What spring constant should you specify?**Instructions:** Express your answer to two significant figures and include the appropriate units.**Input Box for Answer:** - \( k = \) [Value] [Units]**Submit Button**---#### Part B**Question:** What is the maximum speed of a 320 kg car if the spring is compressed the full amount?**Instructions:** Express your answer to two significant figures and include the appropriate units.**Input Box for Answer:** - \( v = \) [Value] [Units]**Submit Button**

The mass of the car is M = 410 kg. Assume the acceleration due to the gravity of Earth as g = 9.80 m/s2. The height of the hill is h = 11 m. The roller coaster descends down from the top of the hill to its lowest point covers a distance of h1 =18 m. The maximum compression in the spring is x = 2 m. The spring constant must be raised by 11% for safety reasons.(A) Find the spring constant ( k' ) of the spring using the relation: Mgh=12kx2410×9.80×11=12k2244198=2kk=22099 N/m Increase the value of spring constant by 11% for safety reasons, k'=22099+1110022099k'≈24530 N/m Hence, the spring constant of the spring should be specified as 24530 N/m. (B) Assume the mass of the car is m = 320 kg. Find the maximum velocity (v) of the car when the spring is compressed to its full amount, using the relation: 12kx2=mgh1-h+12mv2kx2=2mgh1-h+mv2v=kx2m-2gh1-h Substitute the values, v=2453022320-29.8011-18v=306.625+137.2v=21.06 m/s Hence, the maximum velocity (v) of the car when the spring is compressed to its full amount, is 21.06 m/s.

Science

Physics

You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 11-m-high hilI, then descends 18 m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.0 m and that a loaded car will have a maximum mass of 410 kg. For safety reasons, the spring constant should be 11% larger than the minimum needed for the car to just make it over the top.

You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 11-m-high hilI, then descends 18 m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.0 m and that a loaded car will have a maximum mass of 410 kg. For safety reasons, the spring constant should be 11% larger than the minimum needed for the car to just make it over the top.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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