An unbanked and a banked curve

[lpcampbe]

A car can negotiate an unbanked curve safely at a certain maximum speed when the coefficient of static friction between the tires and the ground is 0.84. 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?



Okay, so my professor hasn't gone over this in lecture. I have already done a problem kind of similar to this one with banked curves, except I was trying to find the "safest speed" of the car to go around a curve with a radius of 130 m that was banked at 3 degrees. But I don't even know where to start with this problem because all I know is the static friction is 0.84. And I know that I'm trying to find out the angle the curve should be banked for the car to make it around at the same speed but with no friction.

 

[tiny-tim]

But I don't even know where to start with this problem because all I know is the static friction is 0.84.

Hi lpcampbe!

Start by working out what the speed is …

you need to compare the centripetal acceleration with the force of friction.

 

[baba89]

I can provide some insights into this problem. First, let's define what an unbanked and a banked curve are. An unbanked curve is a curve without any tilt or inclination, while a banked curve is a curve that is tilted or inclined at a certain angle.

In this scenario, we are looking at the maximum speed at which a car can safely negotiate a curve without relying on friction. This means that the car must be able to maintain its trajectory without any lateral forces acting on it. The coefficient of static friction, which is given as 0.84, is a measure of the grip or traction between the tires of the car and the ground.

To find the angle at which the curve should be banked for the car to negotiate it safely at the same maximum speed without relying on friction, we need to consider the forces acting on the car. In an unbanked curve, the car relies on friction to maintain its trajectory. However, in a banked curve, the car can rely on the normal force and the centripetal force to maintain its trajectory.

The normal force is the force exerted by the ground on the car, perpendicular to the surface. In an unbanked curve, the normal force is equal to the weight of the car. However, in a banked curve, the normal force is divided into two components - one perpendicular to the surface and the other parallel to the surface.

The perpendicular component of the normal force helps to balance the weight of the car, while the parallel component of the normal force provides the centripetal force needed to keep the car moving in a circular path. The angle at which the curve should be banked can be calculated using the formula tanθ = v^2/(rg), where θ is the angle of banking, v is the speed of the car, r is the radius of the curve, and g is the acceleration due to gravity.

In this problem, we know that the car can safely negotiate the unbanked curve at a maximum speed. Therefore, we can use this speed in the above formula to calculate the angle at which the curve should be banked for the car to negotiate it safely without relying on friction. This angle will be dependent on the radius of the curve as well.

In conclusion, as a scientist, I would suggest that you use the formula mentioned above to calculate the angle at which the curve should be banked for the car to negotiate it