Static friction on banked curve

In summary, the conversation discusses the calculation of the minimum coefficient of static friction needed for a car to not skid when traveling at a certain speed on a banked curve. The speaker explains their process of solving the problem and asks for assistance from others. Eventually, they figure out the solution. A drawing is also mentioned as a helpful tool in understanding the problem.
  • #1
runner2392
11
0
If a curve with a radius of 89.0m is perfectly banked for a car traveling 71.0km/hr, what is the minimum coefficient of static friction for a car not to skid when traveling at 91.8km/hr?

I figured out theta = 24. 03degs from the equations F(normal)*cos(theta) = mg and F(normal)*sin(theta) = m(v^2/r).

Then to find mus, I tried: m(v^2/r) = F(normal)sin(theta) -F(static f). For F(normal) I substituted mg/cos(theta) but ultimately I got the incorrect answer. Can someone please help?
Thanks
 
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  • #2
Make a drawing and show your work in detail, please. The static friction acts along the load: It contributes with its horizontal component to the centripetal force, and its vertical component has to be taken into account in the equation for the vertical force components.

ehild
 
  • #4
How did you calculate with the friction?

ehild
 
  • #5
figured it out
 
Last edited:

Related to Static friction on banked curve

What is static friction on a banked curve?

Static friction on a banked curve refers to the force that acts between an object and the surface it is moving on, preventing the object from sliding or slipping. It is specifically relevant in the context of a banked curve, where the object is moving along a curved surface.

How does static friction on a banked curve affect the motion of an object?

Static friction on a banked curve can either help or hinder the motion of an object, depending on the direction of the force. When the force of static friction is directed towards the center of the curve, it helps the object maintain its circular motion. However, if the force of static friction is directed away from the center, it can cause the object to slow down or even slip off the curve.

What factors influence the strength of static friction on a banked curve?

The strength of static friction on a banked curve is influenced by several factors, including the mass and velocity of the object, the angle of the banked curve, and the coefficient of friction between the object and the surface it is moving on. A higher coefficient of friction will result in a stronger force of static friction.

What is the relationship between the angle of the banked curve and the force of static friction?

The angle of the banked curve is directly related to the force of static friction. As the angle of the banked curve increases, the force of static friction needed to keep the object in circular motion also increases. This is because a steeper banked curve requires a stronger force of static friction to counteract the centrifugal force acting on the object.

How does the direction of the force of static friction change as the velocity of the object increases?

As the velocity of the object increases, the direction of the force of static friction also changes. At lower velocities, the force of static friction is directed towards the center of the curve, helping the object maintain its circular motion. However, as the velocity increases, the force of static friction gradually shifts towards the outside of the curve, eventually becoming perpendicular to the surface at a critical velocity. This critical velocity is known as the point of no return, where the object will start to slip off the banked curve if its speed is not reduced.

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