Finding the Angle for Safe Max Speed on Unbanked Curve

In summary, the car can safely negotiate an unbanked curve at a certain maximum speed when the coefficient of static friction is 0.88. To safely negotiate the same curve at the same maximum speed without relying on friction, the angle of the curve should be calculated using the equations v^2 = gr*((sinQ + μcosQ)/(cosQ - μsinQ)) and NycosQ = mg + fsinQ. The first equation is used to find the speed, while the second equation is used to find the angle.
  • #1
aimslin22
51
0
A car can negotiate an unbanked curve safely at a certain max speed when the coefficient of static friction between the tires and the ground is 0.88. At what angle should the same curve be banked for the car to negotiate the curve safely at the same maximum speed without relying on friction?


Homework Equations



Normal force = N
angle = Q
friction = f

NycosQ = mg + fsinQ

NxsinQ + fcosQ = mvˆ2/r

The Attempt at a Solution


Both equations simiplify to:

vˆ2 = gr*((sinQ + μcosQ)/(cosQ - μsinQ))

I know I am suppose to find the speed first, which I have no idea how to find. Then, how would I find the angle?
 
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  • #2
Hi aimslin22,

What is the angle for the first situation (the unbanked curve)? What is the coefficient of friction for the second situation (the banked curve)?
 
  • #3
That was all the info I was given, but my teacher went over it today. Thanks though!
 

FAQ: Finding the Angle for Safe Max Speed on Unbanked Curve

1. What is the purpose of finding the angle for safe max speed on unbanked curve?

The purpose of finding the angle for safe max speed on unbanked curve is to determine the maximum speed at which a vehicle can safely travel on a curve without losing control or sliding off the road.

2. How is the angle for safe max speed on unbanked curve calculated?

The angle for safe max speed on unbanked curve is calculated using the equation: θ = tan^-1 (v^2 / rg), where θ is the angle of the curve, v is the speed of the vehicle, r is the radius of the curve, and g is the acceleration due to gravity.

3. What factors affect the angle for safe max speed on unbanked curve?

The angle for safe max speed on unbanked curve is affected by various factors such as the weight and size of the vehicle, the condition and type of tires, the road surface, and the weather conditions.

4. How does the angle for safe max speed on unbanked curve differ from banked curve?

The angle for safe max speed on unbanked curve is different from banked curve because banked curves have a slope that helps to counteract the centrifugal force on the vehicle, allowing for higher speeds, while unbanked curves do not have this slope and require a lower maximum speed to maintain control.

5. Why is finding the angle for safe max speed on unbanked curve important?

Finding the angle for safe max speed on unbanked curve is important because it ensures the safety of both the driver and any passengers in the vehicle. By determining the maximum safe speed, drivers can avoid accidents and maintain control of their vehicle while navigating curves on the road.

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