Centrifugal force vs Gravity

In summary: Where v is the tangential velocity at the point on the curve and r is the radius of the circle.The force is the Centripetal Force - which is just a fancy name for the Force needed to make something travel in a circle (or keep something travelling in a circle). So the Centripetal Force is the net force towards the centre of the circle.F = mv²/rSo now lets look at the car going around the corner. If the car is not sliding then the forward force on the car (from the engine) is balanced by the backward force due to friction between the tyres and the road. This is the static friction force.However, if the car is sliding then the
  • #1
lendav_rott
232
10

Homework Statement


The friction coefficient between the tires and the road is 0.6. What is the maximum velocity of the car without it sliding out of the turn. The radius of the curve is 80m. The curve is considered to be horizontal (as ridiculous as it may sound)

Homework Equations


F = ma

The Attempt at a Solution


Does the assignment imply that the centrifugal acceleration needs to overcome the gravitational acceleration?

If so then can I say that the centrifugal force has to be equal or less than the friction force between the tires and the road?

Fcf = ma = mv²/r
Ff = μmg cosα - but the road is horizontal so α is 0 and Ff = μmg

mv²/r = μmg
v²/r = μg => v = (μgr)^0.5 ≈ 21,7 (m/s)

Is this the correct assumption to be made? What exactly happens when the car starts sliding? Is that the same logic why water will stay in the bucket not fall out if you rotate the bucket quick enough?

This also made me think of the pilot training gadget - you know the centrifugal thing that creates overload. Does overload mean the centrifugal acceleration IS greater than the gravitational acceleration?
How would I determine the speed of the training device if I know the radius and that it would have to, say, create 5 times overload?
Does it mean that the person's weight is 5 times greater in relation to normal weight. eg. 5mg = m(g+a) ?
 
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  • #2
The curve is considered to be horizontal (as ridiculous as it may sound)

Not sure why you say it's ridiculous? Many roads are flat and some even have have "adverse camber".

Does the assignment imply that the centrifugal acceleration needs to overcome the gravitational acceleration?

No it asks how fast the car can go before centrifugal force would exceed the maximium frictional force available.

Fcf = ma = mv²/r
Ff = μmg cosα - but the road is horizontal so α is 0 and Ff = μmg
mv²/r = μmg /m
v²/r = μg => v = (μgr)^0.5 ≈ 21,7 (m/s)

You appear to have the right answer but this line..
mv²/r = μmg /m
should just read
mv²/r = μmg

Is this the correct assumption to be made? What exactly happens when the car starts sliding? Is that the same logic why water will stay in the bucket not fall out if you rotate the bucket quick enough?

When the car starts sliding μ might change. Typically μ is different for "static" and "dynamic" friction. Frequently μ falls when something starts sliding. Perhaps you have come across situations where it's hard to get something to move but once it's moving it becomes easier to keep it moving.

No it's not the same a the water in a bucket problem. In that case you need centrifugal force to exceed the force due to gravity (not friction) in order for the water to stay in the bucket.
 
  • #3
This also made me think of the pilot training gadget - you know the centrifugal thing that creates overload. Does overload mean the centrifugal acceleration IS greater than the gravitational acceleration? How would I determine the speed of the training device if I know the radius and that it would have to, say, create 5 times overload?

Sounds like you are talking about one of these...

http://www.thespacereview.com/archive/402a.jpg

These simulate higher than normal g-force on the body. In the lump at the end of the rotating arm there is a seat that can tilt (eg lean over sideways). As it speeds up the seat normally leans over more and more so that the combination of normal gravity and centrifugal force allways acts downwards through the persons body.

If you were to lock the seat so it can't tilt it would feel like you are going around a corner very fast. Perhaps handy if you want to simulate the sideways forces on a racing car driver.

As regards to how fast it has to rotate to simulate 5g... You have to add (vector addition)together the centrifugal force and the regular gravitational force and arrange for the result to equal 5mg.

Note the machine cannot simulate less than 1g.
 

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  • #4
lendav_rott said:

Homework Statement


The friction coefficient between the tires and the road is 0.6. What is the maximum velocity of the car without it sliding out of the turn. The radius of the curve is 80m. The curve is considered to be horizontal (as ridiculous as it may sound)


Homework Equations


F = ma

The Attempt at a Solution


Does the assignment imply that the centrifugal acceleration needs to overcome the gravitational acceleration?

If so then can I say that the centrifugal force has to be equal or less than the friction force between the tires and the road?

Fcf = ma = mv²/r
Ff = μmg cosα - but the road is horizontal so α is 0 and Ff = μmg

mv²/r = μmg /m
v²/r = μg => v = (μgr)^0.5 ≈ 21,7 (m/s)

Is this the correct assumption to be made? What exactly happens when the car starts sliding? Is that the same logic why water will stay in the bucket not fall out if you rotate the bucket quick enough?

This also made me think of the pilot training gadget - you know the centrifugal thing that creates overload. Does overload mean the centrifugal acceleration IS greater than the gravitational acceleration?
How would I determine the speed of the training device if I know the radius and that it would have to, say, create 5 times overload?
Does it mean that the person's weight is 5 times greater in relation to normal weight. eg. 5mg = m(g+a) ?

On difficulty you are presenting to yourself is the use of the description "centrifugal acceleration" and "Centrifugal Force".

There is no such thing as "centrifugal force".
 
  • #5
So is it referred to as Force of centrifugal acceleration in English?
 
  • #6
lendav_rott said:
So is it referred to as Force of centrifugal acceleration in English?

There is no Centrifugal Acceleration either.

You are after Centripetal Force - a Force towards the centre of the circle, not some imaginary force outwards.
The acceleration is referred to as Centripetal Acceleration - and is inwards, not outwards.

You probably think it should be outward, since that seems to be the direction you would fall if you tried to stand on the tray of a truck while it went around a corner [unless you braced yourself to prevent falling].
But consider this: If you stood on the tray of a truck and it suddenly accelerated forwards, what direction would you fall [relative to the truck]?
 
  • #7
Oh, right, I would fall opposite to the truck's direction and if it went around the corner the force would be pointed towards the center of the corner and I would fall in the middle of the street ...kind of maniacal examples, but I think I understand it - it's Newton's law of motion. The body will attempt to maintain its direction of moving or not-moving if influenced by other forces.
 
  • #8
lendav_rott said:
Oh, right, I would fall opposite to the truck's direction and if it went around the corner the force would be pointed towards the center of the corner and I would fall in the middle of the street ...kind of maniacal examples, but I think I understand it - it's Newton's law of motion. The body will attempt to maintain its direction of moving or not-moving if influenced by other forces.

Much better way of thinking.

Fortunately/unfortunately you will get the correct sized, numerical answer if you assume there is a Centrifugal Force - but the direction will be wrong, and your descriptions will be full of rubbish.
 
  • #9
lendav_rott said:
Oh, right, I would fall opposite to the truck's direction and if it went around the corner the force would be pointed towards the center of the corner and I would fall in the middle of the street ...kind of maniacal examples, but I think I understand it - it's Newton's law of motion. The body will attempt to maintain its direction of moving or not-moving if influenced by other forces.

As for the water in the bucket ...

There is nothing mystical about the size of the acceleration due to gravity. There is no barrier involved.

If you hold a stone in one hand, with your other hand beside that stone, then drop the stone, it is very easy to accelerate you other hand down at a much greater rate than the falling stone. In other words you can easily make something accelerate at a higher rate than gravity.

If you rotate a bucket of water in a vertical circle, you can easily do it such that the centripetal acceleration is greater than 9.8 ms-2.

If you were to have someone photograph you while the bucket is at its highest point, it would look like the water should fall out - since the bucket would appear to be stationary, and thus not accelerating.

If you held the bucket in that position, the water would indeed fall out. The bucket would be stationary while the water was accelerating down at a rate of 9.8 ms-2.

But while you spin the bucket, you may be forcing the bucket to accelerate [towards the centre] at a rate of 12 ms-2. The water in the bucket must also accelerate at that rate - or else the bucket will somehow overtake the water?

Only by having the bucket push on the water can the acceleration of the water be increased from the 9.8 ms-2 it would have if merely falling to the 12 ms-2 it must have to travel with the accelerating bucket. Only if the water stays in the bucket can the bucket apply that extra push needed.

Remember, most [all?]of the acceleration of the bucket of water has to do with a changing direction of velocity, not necessarily a change in magnitude of velocity.
 
  • #10
Appologies for my very lax posts earlier that refer to centrifugal force. PeterO is correct, it's much better to think in terms of centripetal acceleration and that it allways acts towards the center.
 
  • #11
lendav_rott said:
Oh, right, I would fall opposite to the truck's direction and if it went around the corner the force would be pointed towards the center of the corner and I would fall in the middle of the street ...kind of maniacal examples, but I think I understand it - it's Newton's law of motion. The body will attempt to maintain its direction of moving or not-moving if influenced by other forces.

That "which way would I fall" test is a handy way of reminding yourself of the direction an object is accelerating.
 

1. What is the difference between centrifugal force and gravity?

Centrifugal force is a fictitious force that arises when an object is moving in a curved path. It is directed away from the center of rotation and is proportional to the mass and speed of the object. On the other hand, gravity is a force of attraction between two objects with mass. It is always directed towards the center of mass and is proportional to the masses of the objects and the distance between them.

2. Can centrifugal force and gravity cancel each other out?

No, centrifugal force and gravity are two distinct forces that act independently on an object. They cannot cancel each other out because they have different directions and are caused by different physical phenomena.

3. Which force is stronger, centrifugal force or gravity?

The strength of centrifugal force and gravity depends on various factors such as the mass and speed of the object, the distance between objects, and the shape of the path. In most cases, gravity is a much stronger force than centrifugal force.

4. Can centrifugal force cause objects to float in space?

No, objects do not float in space because of centrifugal force. In space, objects appear to float because they are in a state of constant freefall due to the absence of any opposing force like friction. In fact, the centrifugal force created by the rotation of a spacecraft is often used to simulate gravity for astronauts.

5. How does centrifugal force affect the human body?

Centrifugal force can cause a sensation of weight and pressure on the body when experiencing circular motion, such as on a roller coaster or in a high-speed turn. It can also cause dizziness or disorientation. However, the effects of centrifugal force on the human body are temporary and not harmful as long as the force is not too strong.

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