Deriving Formulas for Vmin & Vmax on Glare Ice w/ Zero Friction

In summary, the conversation discusses the design of a circular curve on a new highway, where a car traveling at a certain speed must be able to safely negotiate the turn on glare ice. The discussion also mentions that if the coefficient of static friction increases, the car can travel at any speed within a range from vmin to vmax. The homework task is to derive formulas for vmin and vmax using mu, v, R, and g. The student has attempted to solve the problem but has not been successful.
  • #1
fineztpaki
13
0

Homework Statement



A circular curve of radius R in a new highway is designed so that a car traveling at speed v can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from vmin to vmax. Derive formulas for vmin and vmax using mu for µ, and v, R, and g as appropriate.

Vmin= ?
Vmax= ?

Homework Equations


How can i derive a formula for this?


The Attempt at a Solution


I've tried a couple but I don't know exactly how to do it. When i put my answer it comes out wrong. help?
 
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  • #2
I got for vmin:
Vsqrt((1-mu(Rg)/(V^2))/(1+mu(V^2)/(Rg)))
but it keeps saying its wrong!??!?
 

FAQ: Deriving Formulas for Vmin & Vmax on Glare Ice w/ Zero Friction

How do you derive formulas for Vmin and Vmax on glare ice with zero friction?

To derive the formulas for Vmin and Vmax on glare ice with zero friction, you need to understand the principles of Newton's laws of motion and the concept of coefficient of friction. The formulas can be obtained by setting the net force on an object equal to zero and solving for the maximum and minimum velocities. It is also important to consider the surface area of the object and its mass in the derivation process.

What is the significance of deriving formulas for Vmin and Vmax on glare ice with zero friction?

The formulas for Vmin and Vmax on glare ice with zero friction are important in understanding the behavior of objects on slippery surfaces. They can help predict the maximum and minimum speeds at which objects can move without experiencing any friction or resistance. This information is useful in various fields such as transportation, sports, and engineering.

Can the formulas for Vmin and Vmax on glare ice with zero friction be applied to all objects?

The formulas for Vmin and Vmax on glare ice with zero friction are applicable to objects that have a relatively small surface area and are moving on a flat surface. They may not accurately predict the behavior of larger or irregularly shaped objects. Additionally, the formulas assume that the surface of the ice is perfectly smooth, which may not always be the case in real-life scenarios.

How does the surface area of an object affect the formulas for Vmin and Vmax on glare ice with zero friction?

The surface area of an object plays a crucial role in determining the maximum and minimum velocities on glare ice with zero friction. Objects with a larger surface area experience more air resistance, which can affect their speed. As the surface area increases, the maximum and minimum velocities decrease due to the increased air resistance.

Are there any practical applications of the formulas for Vmin and Vmax on glare ice with zero friction?

Yes, there are several practical applications of these formulas. For example, they can be used in designing faster and more efficient vehicles for transportation on icy roads. They can also be used in sports training to understand the optimum speed and angle for a skater or a skier to move on glare ice. Additionally, these formulas can help engineers in designing equipment and machinery that operate on slippery surfaces.

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