Static Friction and Circular Motion problem

[Coastal]

Homework Statement

Part 1: Rounding a flat, unbanked curve, which has a radius (r), the coefficient of static friction between the car and the road is 0.5. Find the max speed you can take the curve without sliding.

Radius (r) = 25 m

I'll be using (Us) to denote the coefficient of static friction.

Part 2: If the curve is banked at some angle (theta), find theta so that no frition is required to make the curve.

Homework Equations

fsmax = Us * N
N= mg
NcosTheta = mg
NsinTheta = mv²/r

The Attempt at a Solution

For the first part, I concluded that any sideways motion would be the sliding of the car. So static friction has not exceeded maximum friction. So Us < Fsmax. Since there's no vertical motion, N = mg. I figured when the car is about to skid (the max speed) Us = Fsmax.

I came up with the equation: V = √(Us * r * g). Plugging in the #s I got √(.5 * 25m * 9.81m/s²). Which gave me an answer of 11.07 m/s.

Does that sound right?

I'm much more confused with part 2 of the equation. I am assuming the velocity is needed to figure out the angle, so apparently the velocity from part 1 is used. I came up with the equations listed above

NcosTheta = mg
NsinTheta = mv²/r

But if there's no friction at all, wouldn't the angle then have to be zero? I'm really lost on the 2nd part of this problem, but confirmation on the first part would be helpful also.

Thanks.

 

[Mathgician]

look at the two equations you have, what can you do with them? Do you see any common variables on both equations? Do those common variables effect the angle? What does the force of friction do? what direction is friction force facing?

 

[denverdoc]

Homework Statement

[bPart 1: Rounding a flat, unbanked curve, which has a radius (r), the coefficient of static friction between the car and the road is 0.5. Find the max speed you can take the curve without sliding.

Radius (r) = 25 m

I'll be using (Us) to denote the coefficient of static friction.

Part 2: If the curve is banked at some angle (theta), find theta so that no frition is required to make the curve.

I'm much more confused with part 2 of the equation. I am assuming the velocity is needed to figure out the angle, so apparently the velocity from part 1 is used. I came up with the equations listed above

NcosTheta = mg
NsinTheta = mv²/r

But if there's no friction at all, wouldn't the angle then have to be zero? I'm really lost on the 2nd part of this problem, but confirmation on the first part would be helpful also.

Thanks.

Re part two. No, not flat. Look at oval auto racing, they have banks, not because the tires lack friction but everyone wants faster. Is there a way to use that principle so that gravity helps offset the tendency to lose control?

 

[Coastal]

The common variables are the Normal force and the mass, neither of which would effect the angle. The thing I could think of would be combining the equations, since sin divided by cos equals tangent. The normal forces would cancel out resulting in the equation

tanTheta = v² / rg

But where does friction play a role in this? The way I see it if friction is supposed to be zero, even if it was part of the equation, it would zero that side of the equation and force the angle to be zero.

 

[Coastal]

Maybe it's the way I'm looking at it, but if there's no friction, the car would slide immediately. So isn't it impossible to take a curve without friction, even if it is banked at an angle?

Is this a trick question

 

[rootX]

Homework Statement

Part 1: Rounding a flat, unbanked curve, which has a radius (r), the coefficient of static friction between the car and the road is 0.5. Find the max speed you can take the curve without sliding.

Radius (r) = 25 m

I'll be using (Us) to denote the coefficient of static friction.

Part 2: If the curve is banked at some angle (theta), find theta so that no frition is required to make the curve.

Homework Equations

fsmax = Us * N
N= mg
NcosTheta = mg
NsinTheta = mv²/r

The Attempt at a Solution

For the first part, I concluded that any sideways motion would be the sliding of the car. So static friction has not exceeded maximum friction. So Us < Fsmax. Since there's no vertical motion, N = mg. I figured when the car is about to skid (the max speed) Us = Fsmax.

I came up with the equation: V = √(Us * r * g). Plugging in the #s I got √(.5 * 25m * 9.81m/s²). Which gave me an answer of 11.07 m/s.

Does that sound right?

I'm much more confused with part 2 of the equation. I am assuming the velocity is needed to figure out the angle, so apparently the velocity from part 1 is used. I came up with the equations listed above

NcosTheta = mg
NsinTheta = mv²/r

But if there's no friction at all, wouldn't the angle then have to be zero? I'm really lost on the 2nd part of this problem, but confirmation on the first part would be helpful also.

Thanks.

drawing a FBD really helps. Try that way, that may help

 

[Coastal]

Alright, I think I got an answer.

tanTheta = V²/rg = Us*m*g

Theta = Tan -1 (V²/rg) = 26.6 degrees.

Since mass isn't really a factor, I tested the answer with the equation tanTheta = Us*m*g. Us = tanTheta / m*g.

tan26.6 / 800kg(arbitrary)*9.81m/s² = Us = .00006 which is basically insignificant.

Does this look okay?