# Finding location of turning points. Potential Energy?

• Patdon10
In summary, the roller coaster will continue on its uphill trajectory until reaching a point where kinetic energy is converted to potential energy. This point, at (41.39 m, 23.89 m), is where the track should be changed to utilize the potential energy and prevent the roller coaster from slipping backwards.
Patdon10

## Homework Statement

On the segment of roller coaster track shown in the figure, a cart of mass 233.7 kg moves from left to right and arrives at x = 0 with a speed of 16.5 m/s. Assuming that dissipation of energy due to friction is small enough to be ignored, where is the turning point of this trajectory?

x = ?
y = ?

## Homework Equations

Ke_i + Pe_i = Ke_f + Pe_f

## The Attempt at a Solution

This problem is really tough, and I really have no idea where to start. I know the turning point is where the derivative of the function is at a max or min. The only point in that happens which looks to be about (17m, 4m).

I don't know how to I would incorporate kinetic energy into this, but I'm pretty sure I have to. Can anyone push me in the right direction?

In an ideal situation the roller coaster will continue on its uphill trajectory until it loses all kinetic energy and it is converted to potential energy. This is the point where you will want to change the track so that the rollercoaster uses its potential energy and doesn't slip backwards down the track.

x= 41.39 m
y=23.89 m

## 1. What is the significance of finding the location of turning points?

Finding the location of turning points in potential energy is important because it allows us to understand the behavior and stability of a system. It can also provide insights into the forces acting on the system and help us make predictions about its future behavior.

## 2. How is the location of turning points determined?

The location of turning points can be determined by taking the derivative of the potential energy function and setting it to 0. The resulting value(s) represent the points where the potential energy changes from increasing to decreasing or vice versa.

## 3. Can turning points be found for any type of potential energy function?

Yes, turning points can be found for any type of potential energy function, whether it is linear, quadratic, or more complex. The method for finding them may vary, but the concept remains the same.

## 4. How do turning points relate to equilibrium points?

Turning points and equilibrium points are closely related. In fact, equilibrium points are a type of turning point where the potential energy is at a minimum or maximum. The location of turning points can help us determine the stability of an equilibrium point.

## 5. Can finding the location of turning points help in practical applications?

Yes, finding the location of turning points can be useful in practical applications such as engineering and physics. It can help in designing stable structures and predicting the behavior of systems under different conditions.

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