What Is the Minimum Bend Radius for a Car Given Frictional Constraints?

[fcb]

Homework Statement

A certain car experiances a limiting maximum frictional force equal to 75% of its weight. What is the smallest radius of bend that it can move around on a level road at 20ms^-1

Homework Equations

F=mv²/r

The Attempt at a Solution

Couldnt get past last stage.

 

[Astronuc]

What is acting against the centrifugal force?

http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html

http://hyperphysics.phy-astr.gsu.edu/hbase/corf.html#cent

 

[Doc Al]

F=mv²/r

That's Newton's 2nd law applied to circular motion to give you the centripetal force. In this case, what is providing that force? (What is F equal to?) Plug in what you know about F and you'll be able to solve for v.

 

[fcb]

What is acting against the centrifugal force?

http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html

http://hyperphysics.phy-astr.gsu.edu/hbase/corf.html#cent

Thanks for your fast and prompt reply.

That's Newton's 2nd law applied to circular motion to give you the centripetal force. In this case, what is providing that force? (What is F equal to?) Plug in what you know about F and you'll be able to solve for v.

All i know about 'F' is that it is equal to 75% of the cars weight. I don't know the cars mass, How am i able to solve for F? I am lost in my own little world.

 

[Doc Al]

All i know about 'F' is that it is equal to 75% of the cars weight.

Good!

I don't know the cars mass, How am i able to solve for F?

Call the car's mass 'm'. How would you express F in terms of m?

 

[fcb]

Good!

Call the car's mass 'm'. How would you express F in terms of m?

Would it be F=.75 x 'm'

 

[Doc Al]

Would it be F=.75 x 'm'

Almost. Given the mass, how do you calculate the weight?

 

[fcb]

0.75=1x20²/r

0.75=400/r

r=\sqrt{}533

=23.06

 

[fcb]

Almost. Given the mass, how do you calculate the weight?

multiply it by acceleration due to gravity which is 9.8ms^-2

 

[Doc Al]

multiply it by acceleration due to gravity which is 9.8ms^-2

Right. W = mg, where g = 9.8 m/s^2.

So revise your expression for F and plug it into the centripetal force formula.

 

[fcb]

Scrap post #8. Its screwed.

 

[fcb]

7.35=400/r
400/7.35 = 54.42

= 54.42

 

[Doc Al]

7.35=400/r
400/7.35 = 54.42

= 54.42

Good! That radius will have units of m.

Here's how I'd write it:

F = mv^2/r

.75 mg = mv^2/r

The mass cancels (so you don't need to know the mass after all):
.75 g = v^2/r

so: r = v^2/(.75 g)