What is the formula for finding the speed of a roller coaster at point A?

In summary, the conversation discusses finding the velocity of a roller coaster at point A, which has the same height as the starting point. The coaster has an initial velocity of 10m/s, an initial height of 100m, and a mass of 1000kg. The height of point B is half of point A's height, and point C has a height of zero. The equation used to find the velocity at the starting point is vf^2 = vo^2 + 2*a*(xi-xf), where vf is the final velocity, vo is the initial velocity, a is the acceleration, xi is the initial height, and xf is the final height. The conversation also mentions using conservation of energy to find the
  • #1
badtwistoffate
81
0
Roller coaster Vel. Initial=10m/s, Height initial=100m, and the mass of the coaster is 1000kg all at the starting point (*).
Have to find the speed of coaster at point A, point A's height is the same as the starting points, b is 1/2 of a's height, c's height is zero.
Coaster kinda looks like: * is starting point

........../
..._*_..._A_....../
.../----\.../---\..._B_.../
.../------\__/-----\__/----\.../
__/-------------------------\_c_/


I found Vf of the starting point with vf^2=vo^2+2 a deltaH
and used that Vel for Vo when i do it again but for point h.
what should I do?, my Vf of the starting point i got was 45.4m/s
 
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  • #2
vf^2 = vo^2+ 2*a*(xi-xf)

Vo = 10 each time
a = 9.81 each time
xi = 100 each time
xf = height above ground

this should work
 
  • #3
what about conservation of energy?
 
  • #4
I hope ViewtifulBeau realizes that that equation
comes from (as a special case) Energy conservation.

I DO wish you folks would stop treating "g" as an acceleration!
 

What is the Roller Coaster Problem?

The Roller Coaster Problem is a physics problem that involves calculating the forces acting on a roller coaster car as it moves along a track, and determining the maximum speed the car can reach without derailing or causing discomfort to riders.

What factors affect the roller coaster problem?

The factors that affect the roller coaster problem include the design of the roller coaster track, the weight and speed of the car, and the forces of gravity, friction, and air resistance.

How is the maximum speed of a roller coaster calculated?

The maximum speed of a roller coaster is calculated using the principles of energy conservation and centripetal force. The kinetic energy of the car at the top of a hill must be equal to the sum of its potential energy and the energy lost due to friction and air resistance. The centripetal force, provided by the track, must also be able to balance the force of gravity on the car to prevent it from flying off the track.

What safety measures are taken to prevent accidents on roller coasters?

Roller coasters undergo rigorous safety inspections and testing before they are opened to the public. The tracks are designed to withstand high speeds and forces, and safety restraints are used to keep riders securely in their seats. In addition, roller coasters are equipped with various fail-safe mechanisms and emergency brakes to prevent accidents.

Are there any real-world applications of the roller coaster problem?

Yes, the principles used in solving the roller coaster problem are also applied in the design and construction of other structures that involve high speeds and forces, such as bridges and high-speed trains. Understanding the roller coaster problem can also aid in the development of safer and more thrilling roller coasters.

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