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

In summary, during a physics lecture, an example was given about a rubber tire with a static coefficient of one. The calculations showed that at an angle of 45 degrees, the car will start to slide, regardless of the tire area or car mass. This is due to the equal forces in the X direction and the force of static friction. This marks the point between sliding and not sliding, or the beginning of the slide.
  • #1
MRGE
10
0
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?
 
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  • #2
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.
 
  • #3


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!
 

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

1. What is Newton's Law of Friction?

Newton's Law of Friction states that the force of friction between two surfaces is directly proportional to the normal force between the surfaces and the coefficient of friction. It can be represented by the equation Ff = μN, where Ff is the force of friction, μ is the coefficient of friction, and N is the normal force.

2. How does friction affect the motion of an object?

Friction acts in the opposite direction of an object's motion, causing it to slow down or stop. This is because friction is a resistive force that opposes the relative motion between two surfaces in contact. It also causes objects to require more force to overcome it and continue moving.

3. What factors affect the coefficient of friction?

The coefficient of friction is affected by the nature of the two surfaces in contact, the roughness of the surfaces, and the amount of force pressing the surfaces together (normal force). It also varies with temperature and can be affected by the presence of lubricants or other substances between the surfaces.

4. How can we reduce the effects of friction?

Friction can be reduced by using lubricants, such as oil or grease, between the two surfaces in contact. Smooth surfaces also experience less friction than rough surfaces, so polishing or smoothing surfaces can also reduce friction. Additionally, reducing the force pressing the surfaces together can decrease the force of friction.

5. Can friction ever be completely eliminated?

No, friction cannot be completely eliminated. It is a natural force that occurs whenever two surfaces are in contact and is necessary for many everyday tasks, such as walking and driving. However, it can be minimized through various methods, as mentioned in the previous question.

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