Roller coaster velocity at the bottom of an incline

In summary, the problem involves finding the speed of a roller coaster at the bottom of an incline, given its initial speed and distance traveled. The solution involves breaking the weight of the roller coaster into components along and perpendicular to the incline, and using relevant equations to find the acceleration and velocity at the bottom.
  • #1
imatreyu
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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. .
 
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  • #2
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.
 
  • #3
Thank you for clearing it up!
 

FAQ: Roller coaster velocity at the bottom of an incline

1. How is velocity calculated at the bottom of a roller coaster incline?

Velocity at the bottom of an incline can be calculated using the equation v = √(2gh), where v is the velocity, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the incline.

2. Does the mass of the roller coaster affect its velocity at the bottom of an incline?

Yes, the mass of the roller coaster does affect its velocity at the bottom of an incline. A heavier roller coaster will have more inertia, meaning it will require more force to accelerate and therefore will have a lower velocity at the bottom of the incline compared to a lighter roller coaster.

3. How does the angle of the incline impact the velocity of a roller coaster at the bottom?

The angle of the incline does impact the velocity of a roller coaster at the bottom. A steeper incline will result in a higher velocity at the bottom due to the increased potential energy gained during the ascent. However, too steep of an incline can also cause the roller coaster to lose speed and possibly even stop at the top.

4. What factors can affect the velocity of a roller coaster at the bottom of an incline?

Aside from mass and incline angle, other factors that can affect the velocity of a roller coaster at the bottom of an incline include friction, air resistance, and the design of the roller coaster itself. These factors can either increase or decrease the velocity of the roller coaster.

5. Is the velocity of a roller coaster at the bottom of an incline constant?

No, the velocity of a roller coaster at the bottom of an incline is not constant. It will vary depending on the factors mentioned above and can also change throughout the course of the ride due to the design and layout of the roller coaster.

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