Reaction force acting at the wheels of cars when turning

[Like Tony Stark]

Homework Statement

Suppose a car describing a circular trajectory of radius $R$. Consider just a right and left wheel of the car, and suppose that the distance between the two of them is $d$. What's the normal force acting on each of the wheels?

Then answer: these reactions are greater or weaker than the reactions of a static car

Relevant Equations

$F=ma$

Well, I considered the two wheels as two different bodies and I wrote Newton's equations for both of them
I considered the wheel closer to the centre of the circle, we have:
$\mu N_1 =mR\dot (\theta)$
So we can find $N_1$

Doing the same thing, we can find $N_2$
$\mu N_2 =m(R+d) \dot(\theta)$

Then, the more velocity, the more normal needed for the friction. So when it's static the normal are smaller.

 

[BvU]

$\mu N$ is the maximum friction force. Does not have to be the acting friction force.

 

[Like Tony Stark]

$\mu N$ is the maximum friction force. Does not have to be the acting friction force.

So what would it be the right way of calculating it?

 

[haruspex]

It is not entirely clear, but I think the question is asking about forces on the wheels as bodies separate from the car and axles connecting them.
If so, "normal force" means the net normal force on a wheel, i.e. that component of the net force on the wheel which is parallel to the wheel's axis.
For this purpose, you do not need to separate out frictional force (which may anyway have a component in another direction).

Btw, what do you mean by $R\dot(\theta)$? If you mean $R\dot\theta$, what dimension should that have?

 

[jbriggs444]

My interpretation of the question is that it is suggesting that you think about what prevents the car from tipping over.

You are not given enough information to compute a numeric answer. But you are not asked for a numeric answer.

 

[haruspex]

My interpretation of the question is that it is suggesting that you think about what prevents the car from tipping over.

You are not given enough information to compute a numeric answer. But you are not asked for a numeric answer.

Yes, you are right - it is about the forces normal to the ground, i.e. vertical. In this context, merely specifying normal is ambiguous.

 

[BvU]

So what would it be the right way of calculating it?

Start with a drawing: rear view of a car in a turn. Draw the forces and where they act, too