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Homework Help: Speed faster or Lower than speed limit on rough banked ramp.

  1. Nov 12, 2012 #1
    1. The problem statement, all variables and given/known data
    What happens if you enter a banked rough ramp with a speed lower or higher than the speed limit

    2. Relevant equations

    3. The attempt at a solution

    If you enter the ramp with a speed greater than the speed limit the car will spin out of the curve due to the forces contributing to centripetal force are not great enough to keep the car on the ramp (less than the centrifugal force) and the car spins lose. I thought about this like when on Forza motorsport and you are to fast entering a curve and you just can't make the turn and hit into the sides. When you are too slow fnsin(theta) and ffscos(theta) are much stronger than the force that is pulling you outward, centrifugal force, and you will fall into the ramp. When i say centrifugal force, i am referring to the forces that pull the car outward opposite to the centripetal force.
  2. jcsd
  3. Nov 12, 2012 #2


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    Looks good! I would change "into the ramp" to "down the ramp".
  4. Nov 12, 2012 #3
    Hello i answered that question that way, but of course with more detail and a free body diagram, and my teacher gave me 57% on that question, she says that you would slid up or down, and for my question she said that i am saying that centrifugal force is = to fnsin theta and ffscos theta that is why she gave me it wrong. From my perspective of course they are not equal due to other forces acting as well such as air resistance and so forth. She says that if an object is moving to fast on a curve and it spins out it is because of speed not the forces acting outward on it, in this case the centrifugal force. What should i tell her to try to convince her like with facts or proof or anything? Could you please help me?
  5. Nov 12, 2012 #4


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    Wow. Has your teacher any physics qualifications? Of course it's to do with forces.
    That said, it's a good idea never to mention centrifugal force. Such a force is an illusion that results from using an accelerating frame of reference (as might the person whizzing around the curve). From an external observer's "inertial" frame, a body going round a curve needs a centripetal force to make it do so. This force is the resultant of the forces acting on it.
    In the case of a car on a banked curve, there are two sources of the required centripetal force. The normal force has a component acting towards the centre of the curve (unless, of course, the bank is angled the wrong way). How much centripetal force is needed depends on the radius of the curve and the speed. If the bank provides too much or not enough, you'll need static friction from the tyres to make up the difference. If that's not enough you will skid up or down the slope.
    There is another possible failure mode. Even if you don't skid, you might roll. In this case it's a matter of the torque balance.
  6. Nov 13, 2012 #5


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    I am assuming that when you say "the speed limit" you are referring to travelling at the speed which would see you travel around the banking, even if it was smooth rather than rough.
    If that is true then:

    If travelling too fast, the cetripetal force suplied by (a component of) the Normal Reaction Force would be insufficient to complete the curve at the required radius. By travelling in a circle of greater radius, this would require the car to move to a position higher on the banking - effectively sliding sideways across the surface. If the Surface is sufficiently rough, the friction created would be sufficient to prevent that: which actually means that components of the friction force and Normal Reaction Force combine to provide sufficient centripetal force to complete a path of sufficient radius to "drive around the bend".
    If friction is not sufficiently large, the car will still move up the banking [due to travelling in a circle of too large a radius] perhaps eventually hitting the wall at the edge of the track.

    Note: Imagine the track is entirely circular. The radius of the inner edge of the track may be 100m. The radius of the outer [and higher] edge of the track may be 140m.
    You may be attempting to drive half way up the track - where the radius is perhaps 120m.

    If the Normal Reaction Force and friction combine to only provide sufficient force to negotiate a radius of 130m, then your car will move to the position on the track where that is the radius. That is a line further up the track, so the car will appear to slide sideways.

    If the Centripetal Force provided requires a radius of 160m - you are in trouble!!

    If you travel too slowly, the (component of) Normal Reaction force may tend to have you travelling in a circle whose radius is too small. Again, with a rough track, friction can "reduce" the effective centripetal force so that the intended path is maintained.
    If friction is not sufficiently strong, the car will adopt a path of smaller radius - which is lower down the track. So the car will appear to slide down the track.

    There is you full explanation: _ and you will note that Centrifugal Force did not come in to it: because there is no such thing as Centrifugal Force!!!!!!
  7. Nov 13, 2012 #6
    Ok i am confused which of the answers is right.
    Second, how is there no such thing as centrifugal force, if this was the case then we would not be able to separate the components of blood using a centrifuge. Maybe i am not understanding this right please clarify.

    Please read this:
  8. Nov 13, 2012 #7


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    Get ready for a lengthy read here!!

    If you speak to many Geographers, they will tell you that the reason high pressure air systems and low pressure air systems [like cyclones for example] rotate is due to ten Coriolis Force. They call it that because otherwise they couldn't understand the effect caused by the fact we are standing on a spinning earth, not a stationary Earth.
    There is in fact no such thing as a Coriolis Force.

    Similarly, "powermasters" have no idea [or at least little idea] what they are talking about.

    It would be interesting to take someone from that group and have them hold onto the back of a race car, then have that race car accelerate away as fast as is could, and see what force they invented to explain why they were "thrown away from the back of the car". Especially since it would be quite safe for you to stand just behind that person, as they are certainly not going to be thrown into you!!

    Consider the following:


    We know of 3 forces that act without contact:
    Gravitational attraction.
    Electrostatic attraction or repulsion [depends what charges we have]
    Magnetic attraction or repulsion [depends what substances or magnetic Poles we bring together.

    All other forces act by contact.

    Secondly: [a little story]

    A man was walking down the street pulling a long piece of string. A passer-by stopped him and asked "why are you pulling that piece of string?"
    With that the man turned around, and while making a pushing motion to the end of the string in his hand replies "Have you ever tried pushing one?"

    Moral of the story: You can only pull with a piece of string.

    Now the real test:

    It is possibly to attach a set of car keys to the end of a piece of string. This enables you to "twirl" the keys in a horizontal circle above you head.

    The keys are travelling in a circle:
    What direction is the force acting on the keys that enables/causes this to happen.
    [Note: if you release the string, the keys will just fly off in a straight line - we want to know what is causing them to travel in a circle]

    Could it be a Gravitational Force? If you place the keys on a table, and put your hand near the keys, the keys will not move, so if there is a gravitational Force between you and the keys, it is not strong enough for anything to happen.

    Could it be an electrostatic force? I don't think so.

    Could it be a magnetic force? You, and string are certainly not magnetic materials, so that is unlikely.

    So it must be a contact force!!

    What is touching the keys? Answer: the string

    What direction is the contact Force? - and remember: you can only pull with a piece of string!

    Thus we see that the force acting on an object moving in a circle is radially IN.

    It is called the Centripetal Force [powermasters even referred to it].

    There are no other forces acting on the object moving in a circle [because nothing else is touching it!]

    btw: The cetrifuge that the chemists use.
    It operates by accelerating the tubes towards the centre of the device [with a large Centripetal Force. The expanded necks of the tubes jamming in the rings on the device enable that force, and resulting acceleration, to happen.
    The sediment in the liquid in the tubes at first attempts to travel in a straight line rather than in a circle - but only succeeds in reaching the closed end of the tube.
    Once the sediment contacts the closed end of the tube, the contact force between tube and sediment then ensures the sediment travels in a circle like all the other stuff in there.
    The forces involved are really quite high, and the sediment gets quite compacted against the closed end of the tube.
    Once we turn the machine off, and take the tube out, and hold it in the orientation we usually hold such tubes, we see the sediment has gathered on the bottom of the tube.
    Another way to achieve that would be to put the tube in a rack for a couple of days and let the force due to gravity attract the sediment down until it reaches the bottom of the tube. Our feeble intellect thus contrives that in the "centrifuge" some mysterious force must have forced the sediment to the "bottom" of the tubes.
    In fact, the sediment was forced to remain in contact with the closed end of the tube as the only means of receiving enough inward force to travel in the circle that the tube was following.

    A more accurate explanation of what "powermasters" are getting at.

    Get hold of a compass - the drawing instrument with a point on one end and a pencil on the other which is used for drawing circles.

    Place the point in the middle of a sheet of paper and open the compass to a couple of inches [5cm].
    Draw a quarter circle from right of the point, to above the point.
    Open the compass a further couple of cms [or 1 inch], place the point back in the original position and draw the matching quarter circle.

    You now have an example of a bend in a road.

    Now open the compass a few more cms [another inch] and place the compass with the point not in the original position, but further left so that the pencil is on the inner line of your "road"
    Now trace an arc along/across the road.
    About half way around the bend, your last line will cross the outer edge of you road.

    That is the path taken by a car as it "spins out" while travelling too fast for the bend.

    The car was travelling in a circle - it was just that the centripetal force available was only sufficient for the circle to have quite a large radius. There was no "outward" force making the car leave the road, there was just insufficient "inward" force for the car to follow the road accurately.

    Note: explanation of the weather:

    On Earth, air tends to move from the Poles to the equator along the surface, then from the equator to the poles at the top of the atmosphere - it circulates.

    If you could get hold of one of those mounted Globes they often have in Geography rooms
    , you could demonstrate that flow by holding a felt-tip pen on the Pole, against the metal frame that runs beside the Globe, and moving the pen down to the equator.
    That would draw a line along what is know as a meridian of longitude.
    BUT - the Earth is rotating on its axis.

    If, while you were running the pen down the globe, you had a friend rotate the Globe, the line you drew would spiral off to one side.
    Some people see that line and say "look there was a mysterious force causing the air to spiral off to the side!" Then someone decided to call that Force the Coriolis Force. Pity there is no such force.
  9. Nov 13, 2012 #8


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    Just to give the correct answer to their first question

    Hey, do I have a question for you?! What do you think keeps the moon from falling into the earth - what keeps it up there in the sky?

    The moon is in orbit around the Earth. How/why does that work?

    Let's imagine the Earth was a perfect, smooth sphere - so we can do this experiment on the surface.

    If we place a small mass at the edge of a table, and push gently so it falls off the edge, it lands on the floor below the table edge.
    If instead we flicked at that mass, it may hit the floor 1m away from the table.
    Why not flick it harder? It may then land 3 m from the table.
    Now we need to go to our "perfect sphere" Earth.
    Flick even harder, and the mass may land 100m from the table.
    Flick harder!! The mass may land 1 km away.
    MUCH HARDER!!! The mass may land 100km away
    Note - we are not flicking this mass up at all, just horizontally VERY FAST!
    The mass may only take 0.1 seconds to fall from the table to the ground, but as long as we flicked it off at 1000km per second, it will land 100km away.

    FASTER!!! The mass may land 1000km away.
    This is easier than it might seem, because over that distance the curvature of the Earth comes into play and the mass effectively has further to fall, so may take more that 0.1 seconds to reach the ground.

    FASTER!!!!! The mass might actually not hit the ground at all, since the rate at which it falls might be insufficient to match the rate at which the curved surface of the Earth "falls away".
    If we can judge the speed really carefully, the mass will remain the same distance above the Earths Surface at all times - it will be in orbit.

    Of course down here at the surface, Air resistance would ruin everything, but move everything a mere 200km above the surface and there is very little air [and a lot of satellites these days. [The mountains and walls also make this difficult down where we live too.]

    So our mass, all the Satellites, and even the Moon are all accelerating towards the Earth, but they just don't actually get any closer to the surface.
    There is no need for some "Centrifugal Force" to keep them up.
    Indeed if there was a Centrifugal Force balancing the Centripetal Force [supplied by Gravity] the net Force would be zero and the Moon would travel in a straight line, rather than in the circular path it follows around the Earth.
  10. Nov 13, 2012 #9


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    It is very useful to consider centrifugal force in solving problems. The danger is in using both the centripetal and centrifugal forces in the same thinking; you must choose your viewpoint outside the circular motion and use centripetal force OR choose your viewpoint on the thing moving in circular motion and use centrifugal force.
  11. Nov 13, 2012 #10


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    Not a good idea if you are asked where the forces originate, since the centrifugal force is the ficticious Force in one particular accelerating [non-inertial] frame, so has to be creatively invented - but at least in the way thousands before you have invented it.

    Hang your hat on centrifugal force and you are certainly heading for 57% - or less.
  12. Nov 13, 2012 #11


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    I am so sorry to hear it has come to that. Suppose you are asked to calculate the reduction in gravity at the equator of the earth due to the Earth's rotation. You would have a sorry time making it clear without using the dreaded "centrifugal" force. May I assume that when doing calculations with a "centrifuge" you would be allowed some grace?
  13. Nov 13, 2012 #12


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    I wouldn't have said it makes the explanation any more difficult.
    But in the context of the OP this is a rarefied discussion. The teacher, if correctly quoted, gets 5.7% from me.
  14. Nov 13, 2012 #13


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    Good one, haruspex!
    As a high school physics teacher, I found the centrifugal force very important to the students because it was something they could feel. They knew about it from their first ride on a merry-go-round or a car going over a hill at high speed. The centripetal force was more abstract and took some effort to fit into scenarios like that. I think the demo of swinging a pail of water around in the classroom was probably the turning point - it got their attention strongly and they knew very well what would happen if the string broke.
  15. Nov 13, 2012 #14


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    You may imagine your centrifugal force, to get your numeric answer if you please - but you had better not use it in any written explanation of reality.
    btw: The gravity at the equator is lightly less than the gravity at the poles due to the Earth not being a perfect sphere.
    The Normal Reaction Force from the Earth is even further reduced [minutely] due to the circular motion a person is undergoing when standing on the equator [the Earth is rotating].
    Bathroom scales measure that Normal Reaction Force - not the Force of gravity. Those scales often have a scale marked out in Kilograms rather than Newtons as well, as people can't usually comprehend such a large weight figure as 693 N and would prefer to see what sized mass would experience that force.

    On the centrifuge:
    When in operation, the closed end of the tube applies a large centripetal Force on the sediment - provided that sediment is in contact with the fixed end. [I don't like to call it the bottom of the tube, since when the centrifuge is in operation, the closed end of the tube is at roughly the same level at the open neck, so top and bottom are inappropriate.]
    Newton's Third Law will tell you that if the tube is pushing in on the sediment, then the sediment is pushing out on the tube. Perhaps you are thinking that outward force is the Centrifugal Force? However, that force is acting on the glass tube, not the sediment - and I am expecting you wish to refer to the outward force as acting on the sediment when you explain how the centrifuge works. There is no outward force on the sediment.
  16. Nov 13, 2012 #15


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    I weep for your students!!
    There are numerous examples of "child science" - ideas developed in the minds of children to explain the unusual experiences that take place in the tiny percentage of their life spent in a (significantly) accelerating frame of reference.
    As a Physics teacher your role is to attempt to correct their already developed misconceptions.

    They probably think that if a car has a really powerful engine it is capable of pushing them back into the seat when the car accelerates away from a start line or red light.
    I wonder how they imagined the engine did that? Gravity? Electrostatics? Magnetism? because it certainly wasn't a contact force. The only thing touching them was the seat, and that was pushing them forward. What would you have told them?

    And what did the students think was going to happen to the pail of water if the string broke? And did you correct any error there to?
  17. Nov 13, 2012 #16
    Thank you for your help and time overall, it is greatly appreciated! Anyway, i am not understanding, so there is no inertial forces acting in an accelerating system? Like the outward pull when you ride on a merry-go-round, and when you suddenly stop or accelerate in a car. Even in my textbook it is explained using Newton's First Law that an object in rest will remain in rest and an object in motion will remain in motion which ties in with inertia and resistance to a change in motion. Thank you.
  18. Nov 14, 2012 #17


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    Net force = mass * net acceleration.
    On a merry-go-round, at constant angular velocity, you have an acceleration towards the axis of rotation. With no acceleration you would continue at constant linear velocity, i.e. in a straight line. The seat pushes on you, providing a centripetal force and producing that acceleration.
    When a car suddenly accelerates, you won't keep up with that acceleration unless the car pushes you forwards. So at first you don't keep up, and find the seat 'catching up' with you. Only when it has caught up enough will it be pressing hard enough on you to get you up to the same speed.
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