Why Does a Car Slide Downhill at a 45 Degree Incline Despite Equal Forces?

[MRGE]

Ok, I was watching a physics lecture and there was an interesting example given

Heres the Example

"A rubber tire has a static coefficient of one, so at an angle of 45 degrees, the car will start to slide, which is independent of the area of the tires and mass of the car."

So i did the calculations real quick to see if this is true.

For the F (Friction Max) = Coefficient Friction x Normal Force

On an incline:
In the X direction, the Force can be measured in Mass(Gravity)Sin(Theta)
In the Y Direction, the force can be measured in Mass(Gravity)Cos(Theta)

(Correct me if i get any of this stuff wrong)


According to Newton's Law, The force that the car exerts on the ground, the ground as to exert an equal amount of force if the car has no acceleration in the y direction.

So: Mass(Gravity)Cos(Theta) Equals (=) Normal Force (Nf)

And at the Point of Breaking off toe Accelerate, the equation would be:

Mass(gravity)sin(Theta) - F(friction Max) = 0

Substitute F(friction Max) with (static friction = Ms)(Mass(gravity)Cos(Theta))


So you would get

Mass(gravity)sin(Theta) - Ms(M)gCos(theta) = 0

Deriving it from the equation, Than


Tan(theta) = Ms (Static Friction)

Than:

So I plugged Theta = 45 degrees
and 100 kg to those equations

F(Friction Max) = Mu x Normal Force

Tan(45)(100kg)(9.81m/s2)(Cos45) = 693.6717523

The Force in the X direction = (100kg)(9.81m/s2)Sin45 = 693.6717523 also

Since the forces are the same, how can the car move? The forces cancel each other out, granted a tiny force will able to make it slide down but if nothing touches is, the car will still be stationary. So, I can't quite figure out why the professor is saying the car will start to slide down at an angle of 45 degrees since both the Friction Max Force is equal to the X direction Force.

Anyone want to explain this for me?

 

[Delphi51]

Seems to me you explained it yourself! Nice job, too.
Zero force holding it in place marks the point between sliding and not sliding, which you might call the beginning of the slide.

 

[nlightner]

Dear writer,

I can provide an explanation for the example given in the physics lecture. First, let's review Newton's laws of motion. The first law states that an object at rest will remain at rest and an object in motion will continue in motion at a constant velocity unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

In the example given, the car is on an incline and is not moving. This means that the forces in the X and Y directions are balanced, as you correctly calculated. However, when the car starts to move at an angle of 45 degrees, there is now an unbalanced force acting on it - the force of gravity pulling it down the incline. This unbalanced force causes the car to accelerate and overcome the force of static friction, causing it to slide down the incline.

It is important to note that the coefficient of static friction only applies to the maximum force that can be exerted before an object starts to move. Once the object is in motion, the coefficient of kinetic friction applies, which is typically lower than the coefficient of static friction. This is why the car will continue to slide down the incline even though the forces are balanced - the force of kinetic friction is not strong enough to stop the car's motion.

I hope this explanation helps to clarify the example for you. Newton's laws of motion can be complex, but with practice and understanding, they can be applied to many real-world situations. Keep up the good work in your physics studies!