Roller Coaster Problem with Friction

In summary, the problem involves a roller coaster with a height of 35m at point A and 13m at point B. Given a speed of 2.70 m/s at point A and an average force of friction equal to one sixth of its weight, the question is to find the speed at point B. Using the equation for work force of friction, the solution is 24m/s.
  • #1
Bones
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Homework Statement


Suppose the roller coaster in the figure (h1 = 35 m, h2 = 13 m, h3 = 20) passes point A with a speed of 2.70 m/s. If the average force of friction is equal to one sixth of its weight, with what speed will it reach point B? The distance traveled is 35.0 m.
http://www.webassign.net/gianpse3/8-29alt.gif

Homework Equations


Work force of friction = [1/2mv2^2-1/2mv1^2] + [mgh2-mgh1]

The Attempt at a Solution


I took 1/6(9.8m/s^2)(35m) = [1/2v2^2-1/2(2.7m/s)^2] + [(9.8m/s^2)(13m)-(9.8m/s^2)(35m)] and got 23.5m/s which is not correct...what am I doing wrong?
 
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  • #2
Please help I am really frustrated with this one!
 
  • #3
I figured it out, I had the change in height incorrect. V^2 = 2(9.8m/s^2)(35m) + (2.7m/s)^2 - 1/6(9.8m/s^2)(35m)
V=24m/s
 

1. What is the "Roller Coaster Problem with Friction"?

The "Roller Coaster Problem with Friction" is a physics problem that involves calculating the motion of a roller coaster car on a track with friction. It takes into account the forces acting on the car, such as gravity, normal force, and friction, to determine its speed and position at different points on the track.

2. How is friction taken into account in the "Roller Coaster Problem"?

In the "Roller Coaster Problem", friction is taken into account by using the coefficient of friction, which is a measure of the amount of resistance between two surfaces. The higher the coefficient of friction, the more resistance there is and the slower the roller coaster car will move. Friction is also used to calculate the normal force, which is the force that keeps the car on the track.

3. What factors affect the speed of a roller coaster on a track with friction?

The speed of a roller coaster on a track with friction is affected by several factors, including the angle of the track, the height of the track, the mass of the car, and the coefficient of friction. The steeper the track, the faster the car will go due to the force of gravity. A higher track will also result in a higher speed, while a heavier car will move slower due to the increased force of friction.

4. How can the "Roller Coaster Problem with Friction" be solved?

The "Roller Coaster Problem with Friction" can be solved using Newton's laws of motion and the principles of conservation of energy and momentum. The initial conditions, such as the starting height and velocity, and the parameters of the roller coaster, such as the mass and coefficient of friction, are used to calculate the car's speed and position at different points on the track.

5. Are there any real-life applications of the "Roller Coaster Problem with Friction"?

Yes, the "Roller Coaster Problem with Friction" has real-life applications in the design and safety of roller coasters. By accurately calculating the speed and position of a roller coaster car on a track with friction, engineers can ensure that the ride is both thrilling and safe for passengers. This problem also has applications in other fields, such as transportation and robotics, where the effects of friction on motion are important to consider.

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