• petal5
In summary, the conversation discusses how to calculate the smallest radius of curvature for a train going around a curve at a speed of 220km/hr without exceeding the maximum allowed acceleration on the passengers. The formula a=v^2/r is used to calculate the centripetal acceleration experienced by the passengers. The final equation is v^2/r=(0.050)(9.80).
petal5
I've been stuck on this for ages and would appreciate help on how to do it:

On a train, the magnitude of the acceleration experienced by the passengers is limited to 0.050g.If the train is going round a curve at a speed of 220km/hr what's the smallest radius of curvature that the curve can have without exceeding the maximum allowed acceleration on the passengers.

What have you done so far? Hint: What kind of acceleration is experienced when going around a curve?

so far I've attempted to solve using v=r w

Here's another hint: What have you learned about centripetal acceleration?

em,in circular motion direction constantly changes.Centripetal acceleration is the resulting center directed acceleration.

Do I need the formula: a=v^2/r ?

petal5 said:
Do I need the formula: a=v^2/r ?
Yes you do!

When going around a curve, the acceleration is centripetal--that's what they are talking about in this problem.

Be sure to convert everything to standard units before calculating the radius.

How did you arrive at that number?

I said 0.050g=v^2/r (taking v to be 61m/s)

You are forgetting to divide by g, which equals 9.8 m/s^2.

Thanks for all your help!So should my equation be: v^2/r=(0.050)(9.80)

That's right.

petal5 said:
Thanks for all your help!So should my equation be: v^2/r=(0.050)(9.80)
That looks good. Solve the equation for r. You know v. Be careful with your units.

## 1. What is the "problem-smallest radius of curvature" in scientific terms?

The "problem-smallest radius of curvature" refers to the minimum distance from the center of a curved surface to its edge. It is a measure of the amount of bending or curving in a given surface.

## 2. Why is the smallest radius of curvature important in scientific research?

The smallest radius of curvature is important because it can affect the overall shape and properties of a surface. It can also impact the mechanical strength, optical properties, and other characteristics of a material or structure.

## 3. How is the smallest radius of curvature calculated?

The smallest radius of curvature can be calculated using mathematical equations, depending on the type of curve or surface being measured. For example, the radius of curvature for a circle can be calculated by dividing the diameter of the circle by 2, while the radius of curvature for a parabola can be found using the formula (2a^2)/|4a|.

## 4. Can the smallest radius of curvature be negative?

Yes, the smallest radius of curvature can be negative. This means that the center of the curved surface is located on the concave side, and the surface is curving inwards rather than outwards. Negative radius of curvature is commonly seen in concave mirrors and lenses.

## 5. What factors can affect the smallest radius of curvature?

The smallest radius of curvature can be affected by various factors, such as the material properties of the surface, external forces, and the shape and size of the surface itself. Other factors, such as temperature and pressure, can also impact the smallest radius of curvature of certain materials.

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