Roller coaster velocity at the bottom of an incline

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SUMMARY

The discussion focuses on calculating the final velocity of a roller coaster at the bottom of an incline, starting with an initial speed of 4 m/s and descending a distance of 135 ft (41.1 m) at a 40-degree angle. The key to solving the problem lies in understanding the forces acting on the roller coaster, specifically the gravitational force components: mg*sin(40) along the incline and mg*cos(40) perpendicular to it. By applying the equations of motion and neglecting friction, the final velocity can be determined using these forces to find the acceleration along the incline.

PREREQUISITES
  • Understanding of basic physics concepts, particularly forces and motion.
  • Familiarity with trigonometric functions, specifically sine and cosine.
  • Knowledge of kinematic equations for calculating velocity and acceleration.
  • Ability to set up coordinate systems for analyzing forces.
NEXT STEPS
  • Study the derivation of gravitational force components on inclined planes.
  • Learn about kinematic equations in physics for motion analysis.
  • Explore the concept of energy conservation in roller coaster dynamics.
  • Investigate the effects of friction on motion and how to incorporate it into calculations.
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Students studying physics, particularly those focusing on mechanics and motion analysis, as well as educators looking for practical examples of inclined plane problems.

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Homework Statement



A roller coaster starts its descent with an initial speed of 4 m/s. it moves through a distance of 135 ft (41.1 m) along an incline that makes an angle of 40 degrees with the horizontal. Neglect friction and find its speed at the bottom of the incline.

Homework Equations


See below. . .

The Attempt at a Solution



I have the answer, and a process:

http://img707.imageshack.us/img707/9573/picture2la.png However, I don't understand how Fx can possibly equal mg sin40. I don't understand how to set up my coordinate axis so this is possible. I don't even know what Fx is supposed to represent any more. .
 
Last edited by a moderator:
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You have to find the component of the weight(mg) along the inclined plane ( mg*sinθ) and perpendicular to the inclined plane ( mg*cosθ). From that find the acceleration along the inclined plane.

Using the relevant equation find the velocity at the bottom.
 
Thank you for clearing it up!
 

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