# Car on banked road w/ friction

• AHinkle
In summary, the conversation discusses finding the angle theta and radius r in order to keep a car from sliding in a ditch. The equations used are the sum of forces equaling mass times acceleration, the equation for centripetal acceleration, and the equation for friction force. The solution involves using the given values for Vmax, g, and mu, and solving for theta using trigonometry and the equation for centripetal acceleration. The concept of normal force in the x-direction from the bank is also discussed.
AHinkle

## Homework Equations

$$\Sigma$$F=ma
ac=(v^2/r)
f = $$\mu$$N

## The Attempt at a Solution

$$\Sigma$$Fradial= (radial-coordinate of normal force) + (radial component of friction) = ((mass)(velocity^2)/(radius))
$$\Sigma$$Fy= (y-component of normal force) - (y-component of friction) = (mass)(gravity)

$$\Sigma$$Fradial= Nsin$$\theta$$+$$\mu$$Ncos$$\theta$$ = (mv^2/r)
$$\Sigma$$Fy=Ncos$$\theta$$ - $$\mu$$Nsin$$\theta$$ = (mg)

I divided the equations for Fradial by the equation for Fy
and it yielded...

tan$$\theta$$ = (v^2-$$\mu$$rg)/(rg+$$\mu$$v^2)

so in order to find theta which I am looking for

$$\theta$$= arctan (v^2-$$\mu$$rg)/(rg+$$\mu$$v^2)

but I have 2 unknowns...
we know
Vmax = 100km/h which is approx 27.78 m/s
g = 9.81 m/s^2 (this is given in the problem)
r= ?
$$\theta$$ = ?
$$\mu$$= 0.22

also I am not sure how to conceptualize the part of the problem where i need to find out what theta needs to be to keep the car from sliding in the ditch.
I feel i can find the upper limit but not the lower. I thought about subbing something in for r to find theta but I'm stumped.

Last edited:
what do you have so far? If nothing mathematical, what concepts are you thinking about?

im trying to get it to work, and the symbol stuff is screwing up.. how do i delete the post and start over?

Just start A new post I suppose.

okay i fixed everything, please help me out. The homework is already turned in, I just want the knowledge..

think about the x-direction of the normal force from the bank.

## 1. What is a banked road?

A banked road is a road that is curved or angled along its length, as opposed to being flat or level. This is done to help vehicles navigate the road more easily and safely.

## 2. How does a banked road affect a car's motion?

A banked road can affect a car's motion in several ways. If the road is banked, the car will experience a lateral force that helps it turn along the curve. It also reduces the amount of friction between the tires and the road, allowing the car to maintain its speed more easily.

## 3. What role does friction play in a car on a banked road?

Friction plays a crucial role in a car on a banked road. It helps provide the lateral force that allows the car to turn along the curve, and it also helps the tires maintain their grip on the road, preventing the car from sliding or skidding.

## 4. How does the speed of the car affect its motion on a banked road?

The speed of the car can greatly affect its motion on a banked road. If the car is traveling too slow, it may not have enough lateral force to navigate the curve and may veer off the road. On the other hand, if the car is traveling too fast, it may experience a centrifugal force that pulls it away from the curve, causing it to potentially lose control.

## 5. How does the angle of the banked road impact a car's motion?

The angle of the banked road is crucial in determining the amount of lateral force that the car experiences. The steeper the angle, the greater the lateral force, allowing the car to navigate the curve more easily. However, if the angle is too steep, it can also cause the car to experience a higher centrifugal force, which can be dangerous.

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