Engineer Garin's Paraboloid - page 22
You are missing trading opportunities:
- Free trading apps
- Over 8,000 signals for copying
- Economic news for exploring financial markets
Registration
Log in
You agree to website policy and terms of use
If you do not have an account, please register
alsu:
Don't talk nonsense, Alexey :).
TheExpert, deflection from the centre of gravity is impossible without the force of rest friction.
Come on :)))
It is what we use to propel ourselves forward when walking, and it is the only force acting on a person from the external environment in the walking direction.
That's bullshit. It's not applied to the centre of mass. And it is a force - counteracting force resulting from deflection from the axis of application of gravity.
The force of gravity is significantly used (it is the pulling force that causes the friction force), but it acts downwards and thus does not do any useful work. Besides, it is just completely balanced by the support reaction force.
May the year!
Okay. Let's go at it from the other side.
As you know, forces don't come out of nowhere. If an external force acts on a material object, then there is another material object that is its source.
A person moves on the surface. Let's describe the forces:
On the earth side, there's a force of gravity.
Onthe earth side there is a frictional force.
Since the person does not interact with other bodies, there can be no other forces. Everything has to have a cause.
Next, let's have a ball on a string.
The ball interacts solely with the rope. Let's write:
On theside of the string, there is a pulling force on the ball.
Attention, question for the smartest: if there is a mythical force acting on the ball in the direction FROM the centre of rotation, then what itty bitty you so material object causes it?
Physicists have a tradition: every 15 billion years they get together and launch the Large Hadron Collider. ©
And you're twisting the ropes here.
While I have an hour, I will describe the walking process in detail. To make it easier to object, I will number the theses. So.
1. initial position: the person stands at attention on the surface of the planet. His head is free from thoughts. There is a vacuum around. The planet acts on him with two forces: gravitation (downwards) and surface reaction (upwards). Since these forces are balanced, the man is at rest.
2. Suddenly there is an idea in his head - I want to make a step. We will consider it as the initial cause of movement. However, the man does not yet know what mechanism is used to move forward by half a metre. But he knows Newton's laws.
3. The first thought that arises in the mind is to shift one's centre of mass. After all, this is what movement is all about - shifting your own centre of mass. The question is how.
4. Our hero imagines himself without a support in the form of a planet and understands: in such a situation, no matter how much he flounders, he will not be able to shift his centre of gravity. Newton's first law of motion tells him that in order to move the centre of gravity, one must acquire some velocity and, therefore, acceleration (because right now the velocity is zero!). Therefore, to move the centre of gravity from its resting position, an external force must act on it. The question is: where do we get it?
5. Here the dude recalls Newton's third law of motion: in order to make an object act in the right direction, you must act in the opposite direction! So, what have we got at our disposal here? Yep, a surface.
6. So, we have to use the recoil of the surface. He turned out to be educated and immediately decomposed the possible recoil into orthogonal components - parallel and perpendicular to the surface. He doesn't care much about the vertical component - it's necessary to go forward, not upwards. Therefore, it's necessary to get a reaction from the surface, directed in the right direction - forward. If our hero had studied in a Soviet school, he would know that the component of reaction of the support directed along the surface has its own name in mechanics - force of friction at rest. Of course, nothing literally rubs against each other at rest, but a name is a name.
7. In short, we come to the conclusion that we have to force the surface to act on us in the 'forward' direction. How do we do this? Here we have Newton's third law of motion in action: we must act on the support in the "reverse" direction. Simply put, we have to push back. And the normal component of the reaction will make it possible, because for the given two surfaces, the ratio of the maximum possible tangential component and the normal component is a constant, called the coefficient of friction:
max_friction_force = reaction force * coefficient of friction
//I've got a caveat here - in fact, before the transition from rest to slippage.
//there's a small peak in the resting friction force that's higher than the maximum value
// according to this formula. But for this qualitative problem it is immaterial.
8. So, the algorithm is clear: the person acts on the support in the backward direction, the support reacts with an equal modulo force in the forward direction, the result is a slight acceleration forward, the centre of mass shifts.
___________________
Well, you know what happens next. Let's drop a bit, put one foot under, push off with the other (the same mechanism again - friction force in action!) and thus restore the vertical position of the body. Step is taken.
2 alsu
1. Regarding the tipping moments, which are always counted relative to the centre of mass: I called your statement nonsense - forgive my intemperance - I am wrong in form. As for the essence: the moment with respect to the centre of mass is counted in the case of free motion of the body. We have the motion of a system with ties under the influence of forces. In this case, the moments are counted either with respect to anchoring points, supports or contact points. This is known and seemed to me to be self-evident. Draw what there ? I can draw a crane or a cube - by the way there will be no friction force there in your drawing with the cube unless you apply an external force.
2. Concerning school textbooks: from the section "kinematics" it follows that when a body moves along a curvilinear trajectory (let it be a circle for simplicity) it has centripetal acceleration directed towards the instantaneous centre of rotation of the body, which leads to a change in the trajectory of motion. All true, but kinematics does not look at the causes of motion, it looks at it as a given. Schools don't look at the dynamics of systems with couplings under the influence of external forces. Therefore, I am not at all surprised by the simplifications in school textbooks.
3) Now, about the ball on the line: It is true that the movement of the ball on the line is affected by the centripetal force, but this is not the only force. And it is compensated by the centrifugal force.
You have made a completely wrong conclusion from your school course that the only force acting on the ball on the rope is the centripetal force.
That's why you ignore the issue of the tension of the string under the influence of the compressive force. That's understandable: a centripetal force can't tension a string. But what happens? What force is pulling the thread? Where does the centripetal force, which changes the trajectory of motion, come from in the first place? It comes from the tension of the thread, which is due to the forces of inertia of the body, including the centrifugal force, the presence of which you deny. The presence of the centripetal force is a consequence of the tensions that arise in the string under the action of the forces of inertia. That is, this force is derivative and cannot arise by itself. For example, while the drops of fat are floating in the milk, it is not there and the drops of fat go to the walls, where this force appears in the form of an elastic impact on them by the walls of the centrifuge.
And the ball on the string is in a state of apparent equilibrium when it moves evenly around the circumference. In fact, this is not quite the case. So how, what is the system of forces when the ball moves around the circumference ? The answer is as follows:
Since you are very fond of textbook references. Here's a link to excerpts from an academic course on dynamics. The Collins Encyclopedia. Translation. Below is the literature.
http://dic.academic.ru/dic.nsf/enc_colier/6741/%D0%94%D0%98%D0%9D%D0%90%D0%9C%D0%98%D0%9A%D0%90
Since the question started with the presence of centrifugal forces and their place in the system of motion - I highlighted the text in the paragraph about centripetal force.
DYNAMICS
Dynamics studies bodies under the influence of unbalanced external forces, i.e. bodies whose character of motion changes. Since equilibrium means that all forces applied to a body are equal to zero, dynamics obviously deals with forces whose resultant force is not equal to zero. The English physicist and mathematician J. Newton (1643-1727) formulated three laws of motion, to which bodies moving under the action of unbalanced forces obey, and his name is forever attached to these laws.
Newton's first law. Every body maintains its state of rest or uniform and rectilinear motion until unbalanced external forces force it to change its state. It follows from Newton's first law that a body which is in equilibrium remains in equilibrium as long as it is not brought out of equilibrium by external forces.
Inertia. If in order to change the state of rest or uniform and rectilinear motion an external force is needed, something obviously opposes such a change. The inherent ability of all bodies to resist a change in a state of rest or motion is called inertia or inertia. When you have to push a car, it takes more force to get it moving in the beginning than to keep it rolling. Here, inertia manifests itself in two ways. Firstly, as a resistance to the transition from a state of rest to a state of motion. Secondly, if the road is flat and smooth, it is the desire of the rolling car to maintain its state of motion. In such a situation, anyone can feel the inertia of the car themselves by trying to stop it. This would require much more effort than maintaining motion.
Newton's second law of motion. Any body on which a constant force acts will move with an acceleration proportional to the force and inversely proportional to the mass of the body. The most common example of Newton's second law is the fall of a body on the ground. The motion towards the ground is caused by the force of gravitational attraction, which is almost constant at low height of fall. Therefore, for each second that the body falls, its velocity increases by 9.8 m/s. Thus, the falling body moves with an acceleration equal to 9.8 m/s2. Newton's second law of motion is written as the algebraic relation F = ma, where F is the force applied to the body, m is the mass of the body and a is the acceleration caused by the force F.
Impulse (quantity of motion). The quantity of motion of a body is the product of its mass m by its velocity v, i.e. the value mv. The quantity of motion is the same for a car with the mass of 1 ton, rushing at 100 km/h and for a 2-ton truck moving in the same direction at 50 km/h. Since acceleration is the change of velocity in a small time t, Newton's second law of motion can be rewritten as mv = Ft. The product of the force F by the (short) time t was previously called the momentum of the force. Therefore, the quantity of motion is now called momentum. The law of conservation is valid for momentum (quantity of motion): when two or more bodies collide, their total (total) momentum does not change. For example, when hammering a nail with a hammer, the total momentum of the hammer and the nail after impact is equal to the total momentum of the hammer before impact (since the momentum of the nail before impact was zero).
Newton's third law of motion. For every force of action there is an equal but oppositely directed force of counteraction. In other words, whenever one body acts with any force on another, the latter also acts on it with an equal but oppositely directed force. An example of this is the recoil of a rifle when it is fired. The rifle acts on the bullet with a forward force and the bullet on the rifle with a backward force. The result is that the bullet flies forward and the rifle recoils into the shoulder of the shooter. If the force exerted on the bullet is considered an action, the recoil will be a counteraction (reaction). Another example to the third law is the jet motion of a missile. Here the action is the outflow of a jet of gases from the nozzle of the engine, and the counteraction (reaction) is the movement of the rocket in the direction opposite to the movement of the gases.
Centripetal force. When a ball on a string (Fig. 5) is rotated, the string pulls it towards the centre of rotation. The force directed towards the centre of rotation is called centripetal force. The inertia of the ball (its tendency to continue in a straight line at every moment) causes the string to stretch. As the ball continues to rotate in a circle, its inertia creates an equal but oppositely directed, so-called centrifugal force. If the ball moves in a circle at a constant speed, it may appear to be in equilibrium with respect to the centre of the circle. But this is incorrect. In fact, the ball gains acceleration towards the centre of rotation, although it remains at the same distance from the centre at all times. This apparent paradox is explained in Fig. 6. Here the curve AB is part of the circular trajectory of the ball, and the line AC is the tangent (to the circle) along which the ball would fly if the string were broken and it were moving by inertia. The lengths s, t, u and w, connecting the arc and the line, increase in the direction of motion. In order for the ball to keep moving along the circular arc, some force F has to keep it moving with increasing speed. The necessary acceleration is given to it by the centripetal force.
Halfman R. Dynamics. M., 1972 Tatarinov Y.V. Lectures on Classical Dynamics. Moscow, 1984 Newton I. Definitions. Axioms and laws of motion. M., 1985 Babenkov I.S. Fundamentals of Statics and Strength of Materials. М., 1988
And about the theorem theory credits - a finger in the sky ;) .....
VladislavVG:
Centripetal force. When the ball is rotated on the string (Fig. 5), the string pulls it towards the centre of rotation. The force is called centripetal force, which is directed towards the centre of rotation. The inertia of the ball (its tendency to continue in a straight line at every moment) causes the string to stretch. As the ball continues to rotate in a circle, its inertia creates an equal, but oppositely directed, so-called centrifugal force.
Exactly so, although the figure is inaccurate.
The ball acts on the twine with a force away from the centre. The twine acts on the ball by a force directed towards the centre.
This is how Newton's 3rd law is formulated to which you are referring. One body acts on another, the other responds with a force equal in modulo and opposite in direction. But in the end, there is only ONE force acting on the ball - the centripetal force on the side of the string.
You are wrong about the system with links. They do exist and the moments in them are counted exactly as you wrote. But there is one nuance. The whole theory of calculation of these systems appeared only because in them the centre of mass is insignificant due to the static nature of the problem, or in general its position cannot be determined from the conditions. But if the system is in dynamics and there are no rigid links (and here there are none - there is only the contact point), then all the lever calculations must be made relative to the centre of mass.
You guys are so on edge, aren't you?
Seriously, let's move on to the non-trade-related tasks branch.