# Car on circular turn with friction; finding max. velocity

• awertag
In summary, the car can travel at a maximum speed of 9.998 m/s without skidding on a flat road if the coefficient of static friction between the tires and the road is 0.40.
awertag

## Homework Statement

A car of mass 1800 kg rounds a circular turn of radius 10 m. If the road is flat and the coefficient of static friction between the tires and the road is 0.40, how fast can the car travel without skidding?

## The Attempt at a Solution

I thought to do Fnet(c) = (mv^2)/r
Fn-mg= (mv^2)/r
but i thought that for max speed without going off road is when Fn=0
so it would just be mg= (mv^2)/r
which gave me v=9.998 m/s

Was wrong...I don't know what else to do and how to include friction. Any good help will be greatly appreciated. --awe.g

Imagine your car taking a turn. It can, as long as force of the friction serves as a centripetal force (this is indeed the force that makes your car turn ;)). Hence they both have to be equal. Now, the force of the friction is the force that the car applies to the surface of the road multiplied by the coefficient of the friction.

ok so then my frictional force is equal to Fn-mg?
but how does that help exactly?

Why would your frictional force be equal to Fn-mg? your friction force is lesser than or equal to $$\mu F_n$$, $$\mu$$ being friction coefficient. In our case we want our friction force to be as big as it can, hence $$F_f = \mu F_n$$.

oh right. but I thought I want Fn to be 0 because you want to go as fast as possible without going off the road?

Yep, but your car ain't going to fly :P. I mean, increasing velocity increases force neaded for a car to turn and it works only in XY plane. Fn is constant all the time.

lol too bad... I got the question now, thanks for all your help!

## 1. What is the equation for finding the maximum velocity of a car on a circular turn with friction?

The equation for finding the maximum velocity of a car on a circular turn with friction is v = √(μrg), where v is the maximum velocity, μ is the coefficient of friction, r is the radius of the turn, and g is the acceleration due to gravity.

## 2. How does friction affect the maximum velocity of a car on a circular turn?

Friction plays a crucial role in determining the maximum velocity of a car on a circular turn. It creates a resistive force that acts against the car's motion, making it difficult for the car to maintain a high speed. As the coefficient of friction increases, the maximum velocity of the car decreases.

## 3. Can the maximum velocity of a car on a circular turn ever be greater than the velocity of the car on a straight road?

No, the maximum velocity of a car on a circular turn cannot be greater than the velocity of the car on a straight road. This is because on a circular turn, the car needs to overcome the additional force of friction, which will always limit its maximum speed compared to a straight road where there is no additional force acting against the car's motion.

## 4. How does the radius of the circular turn affect the maximum velocity of the car?

The radius of the circular turn has a significant impact on the maximum velocity of the car. As the radius increases, the maximum velocity also increases because the car has a wider turning radius and can negotiate the turn with less resistance from friction. On the other hand, a smaller radius will result in a sharper turn and a lower maximum velocity.

## 5. Is the maximum velocity of a car on a circular turn affected by the mass of the car?

Yes, the maximum velocity of a car on a circular turn is affected by the mass of the car. A heavier car will have more inertia and will require a greater force to maintain a high speed on a circular turn, thus resulting in a lower maximum velocity compared to a lighter car.

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