# Finding Speed on Slippery Curves: R, Theta, Mu

• vivekfan
In summary, the conversation discusses the question of what speed a car should have on a slippery curve in order to eliminate frictional force between the car and the road. Equations and concepts related to centripetal force, gravity, and inclines are mentioned, with a final conclusion that centripetal acceleration should be considered as a horizontal force in this type of problem.
vivekfan

## Homework Statement

A car rounds a slippery curve. The radius of curvature of the road is R, the banking angle is theta and coefficient of friction is mu. What should be the cars speed in order that there is no frictional force between the car and the road?

F=mv^2/r

## The Attempt at a Solution

In general, I have no idea how the components or forces work for banking curves, so an explanation and help would be greatly appreciated.

im not sure about what to do with the bank, but since the force of friction (along with the banking) is providing the centripetal force, set mu*m*g= mv^2/r I'm sorry I can't quite remember what to do with the bank angle.

Centripetal acceleration is a horizontal force. Resolve it into the components on the incline.

Gravity is vertical. Resolve its force components.

If you are gong to ignore friction then the component of gravity down the incline must be balanced by centripetal force up the incline.

is centripetal acceleration always a horizontal force?

looking back from what I recall you should use:

tan(theta)= v^2/rg

I can't really explain it, I am going to review the concept now

vivekfan said:
is centripetal acceleration always a horizontal force?

Yes, for this type problem you should take it as horizontal.

On a roller coaster though it will be radial but in the vertical plane.

## 1. What is R, Theta, and Mu in relation to finding speed on slippery curves?

R, Theta, and Mu are variables used in physics to calculate the speed of an object on a slippery curve. R represents the radius of the curve, Theta represents the angle of the curve, and Mu represents the coefficient of friction between the object and the surface of the curve.

## 2. Why is it important to consider the coefficient of friction when finding speed on slippery curves?

The coefficient of friction (Mu) determines how much resistance the surface of the curve will provide to the object. It is important to consider because it affects the overall speed of the object on the curve. A higher Mu will result in a slower speed, while a lower Mu will result in a faster speed.

## 3. How does the angle of the curve affect the speed of an object?

The angle of the curve (Theta) plays a significant role in determining the speed of an object. A sharper curve with a smaller Theta will require the object to slow down in order to maintain stability and prevent slipping. On the other hand, a wider curve with a larger Theta will allow the object to maintain a higher speed.

## 4. Can the radius of the curve impact the speed of an object?

Yes, the radius of the curve (R) can also affect the speed of an object. A larger radius will result in a gradual curve, allowing the object to maintain a higher speed. A smaller radius will result in a sharper curve and the object will need to slow down to navigate the curve safely.

## 5. How do you calculate the speed of an object on a slippery curve using R, Theta, and Mu?

The formula for calculating the speed on a slippery curve is v = sqrt(R x g x tan(Theta) x Mu), where v is the speed, R is the radius of the curve, g is the acceleration due to gravity, Theta is the angle of the curve, and Mu is the coefficient of friction. Plug in the values for each variable and solve for v to find the speed of the object on the slippery curve.

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