Friction forces and motion resulting from them

[Robittybob1]

I realise I don't fully understand friction.

All things regarding friction discussion welcome here please.

 

Take a mass on a sloped table the friction holds it there. Apply a force from the side and increase the force till it moves.

What direction will it move? Will it always move in the direction of the net force? Not just the direction of the force overcoming the friction.

 

Are the forces of friction always present or do they build up to resist a push?

[studiot]

No one fully understands friction, but certain observations can be drawn that facilitate calculations with it.

 

1) Friction always acts to oppose motion or the tendency to move.

 

2) Friction has two separate zones of operation. A variable zone called static friction and a fixed zone called dynamic friction.

 

3) Friction can change (reverse) direction at the point of beginning to move, you mass on a slope has this quality.

 

4) The force of static friction on an object is only ever enough to oppose an applied force to prevent movement. In the case of zero applied force it is zero.

 

5) The force of static friction can do no work.

 

6) The force of dynamic friction does work.

 

7) The force of dynamic friction is constant regardless of the applied force and less than the applied force.

 

 

 

Note on (3) above

 

Suppose the applied force is pulling or pushing the mass up the slope, but the mass is not moving.

While the mass on the slope is not moving but being pushed up the slope by the tendency is to slip down the slope, pulled down by gravity.

This is static friction and it acts up the slope

 

As soon as the appled force becomes so strong that the mass starts to move upthe slope, the force of friction reverses (opposing the motion) and acts down the slope The friction is now dynamic friction.

[J.C.MacSwell]

 

 

 

Note on (3) above

 

Suppose the applied force is pulling or pushing the mass up the slope, but the mass is not moving.

While the mass on the slope is not moving but being pushed up the slope by the tendency is to slip down the slope, pulled down by gravity.

This is static friction and it acts up the slope

 

As soon as the appled force becomes so strong that the mass starts to move upthe slope, the force of friction reverses (opposing the motion) and acts down the slope The friction is now dynamic friction.

It reverses as soon as the applied force up the slope becomes greater than the gravitational component down the slope, while still in static range, and the mass moves when the applied force becomes greater than the gravitational component and maximum static friction force combined.

[studiot]

Yes, you are right thank you MacSwell.

[Robittybob1]

So when you push from two directions perpendicular to each other but only one force is great enough to overcome friction on its own (assuming the mass has equal friction in all directions), do those two forces combine vectorially based on the amount of the initial strength of two individual forces?

So two forces acting at right angles add together to make a stronger force. Is that right?

[J.C.MacSwell]

So when you push from two directions perpendicular to each other but only one force is great enough to overcome friction on its own (assuming the mass has equal friction in all directions), do those two forces combine vectorially based on the amount of the initial strength of two individual forces?

So two forces acting at right angles add together to make a stronger force. Is that right?

That's correct. When that force is strong enough to overcome the maximum static friction it moves in the direction of the combined vectors.

A free body diagram helps to see what will occur.

[Robittybob1]

That's correct. When that force is strong enough to overcome the maximum static friction it moves in the direction of the combined vectors.

A free body diagram helps to see what will occur.

When the surface an object is sitting on is accelerated from under it the object also slides and accelerates, so is inertia capable of contributing to a type of force, without an external force acting on the inertial mass?

There is the classic pulling the tablecloth from under the place settings.

[Mordred]

RobbityBob1 a tool that may help you understand force vector summing is to use a force vector diagram.

 

The steps are easy, make sure all units are converted to Newtons.

 

Take a protractor and a ruler. Each Newton of force is 1 mm. Or if you need a different scale say 1 cm etc just keep the scale the same in each calculation.

 

So say you wish to sum two forces 1 Newton and say 5 Newtons. One going 0 degrees the other going 96 degrees.

 

Step one. Use protractor measure angle 0 degrees. Then use ruler draw a line 1 cm. Label start a end point b. Then from point b measure angle 96 degrees. Measure 5 cm. Label this point c.

 

draw a line from a to c. Then measure angle from a to c and distance.

 

the alternative obviously is to apply trigonometry. But this method is quick and handy for approximations.

 

http://www.physicsclassroom.com/class/vectors/Lesson-1/Vector-Addition

When the surface an object is sitting on is accelerated from under it the object also slides and accelerates, so is inertia capable of contributing to a type of force, without an external force acting on the inertial mass?

There is the classic pulling the tablecloth from under the place settings.

The cloth requires less force to move than the table or object on top of it. Once the force of the pulling on the cloth is sufficient to move the cloth (and overcome friction) the cloth will move. However there is still insufficient force to move the table or object. So neither the table or object moves only the cloth.

There is one aspect of friction that may help.

 

Coefficient of friction.

 

http://www.engineeringtoolbox.com/friction-coefficients-d_778.html.

 

this will get you started.

 

Engineers handbook has a handy table

http://www.engineershandbook.com/Tables/frictioncoefficients.htm

Friction itself can be categorized into different aspects. Some covered here.

 

http://en.m.wikipedia.org/wiki/Friction

The static friction formula is

 

[latex]F_s=\mu_s F_n[/latex]

 

[latex]F_s[/latex]static friition

[latex]\mu_s[/latex]coefficient of friction

[latex]F_n[/latex] normal force required to move a given mass

Edited May 24, 2015 by Mordred

[swansont]

When the surface an object is sitting on is accelerated from under it the object also slides and accelerates, so is inertia capable of contributing to a type of force, without an external force acting on the inertial mass?

There is the classic pulling the tablecloth from under the place settings.

 

No. You need an external force to accelerate an object. That hasn't changed from the last time you asked. F = ma means a = F/m

 

What's the connection to the tablecloth trick?

[Robittybob1]

 

No. You need an external force to accelerate an object. That hasn't changed from the last time you asked. F = ma means a = F/m

 

What's the connection to the tablecloth trick?

In the tablecloth the force on the objects is the frictional force between the table cloth and the objects on the table. Is this a case of unbalanced forces?

[swansont]

In the tablecloth the force on the objects is the frictional force between the table cloth and the objects on the table. Is this a case of unbalanced forces?

 

Yes. In the horizontal direction the only force is that of friction. It happens quickly, so the impulse imparted to the objects is very small.

[Robittybob1]

 

Yes. In the horizontal direction the only force is that of friction. It happens quickly, so the impulse imparted to the objects is very small.

 

 

Yes. In the horizontal direction the only force is that of friction. It happens quickly, so the impulse imparted to the objects is very small.

How do you relate inertia to this impulse? Are we really talking about change in momentum when we generally talk of inertia?

Is there is a formula linking inertia to force or mass?

[swansont]

How do you relate inertia to this impulse? Are we really talking about change in momentum when we generally talk of inertia?

Is there is a formula linking inertia to force or mass?

In most circumstances, inertia is described by the momentum. Sometimes it means mass.

[Robittybob1]

In most circumstances, inertia is described by the momentum. Sometimes it means mass.

Mass has inertia whether moving or not, so it seems more like mass than momentum. I don't know.

I saw a demonstration of how to place a hammer head on a handle and one method was to use the inertia of the head. I suppose someone else would put it down to the kinetic energy or even the momentum the head had.

[swansont]

Mass has inertia whether moving or not so it seems more like mass than momentum.

 

Mass isn't a substance. An object has mass, and has inertia. If inertia were simply mass, then one would not say a moving object has more inertia than a stationary one. But people do say this.

 

I think what you need to recognize is that the concept of inertia has been refined into mass and momentum. Those are the quantifiable, measurable variables. Those are terms one looks at when solving equations. The term inertia doesn't come up by itself all that often in physics*, outside of the introductory discussion of Newton's first law, which states the principle of inertia. All the heavy lifting, and the doing of real physics, stems from the second and third laws.

 

*it seems to come up a lot in discussion here, while the second and third laws are avoided, because they involve math. But the chances are good you aren't really doing physics if you keep discussing inertia transfer, etc., because you aren't quantifying anything.

[Robittybob1]

 

Mass isn't a substance. An object has mass, and has inertia. If inertia were simply mass, then one would not say a moving object has more inertia than a stationary one. But people do say this.

 

I think what you need to recognize is that the concept of inertia has been refined into mass and momentum. Those are the quantifiable, measurable variables. Those are terms one looks at when solving equations. The term inertia doesn't come up by itself all that often in physics*, outside of the introductory discussion of Newton's first law, which states the principle of inertia. All the heavy lifting, and the doing of real physics, stems from the second and third laws.

 

*it seems to come up a lot in discussion here, while the second and third laws are avoided, because they involve math. But the chances are good you aren't really doing physics if you keep discussing inertia transfer, etc., because you aren't quantifying anything.

That was what I am trying to get my head around. A month ago I put a question into Google, something like "does inertia increase with velocity?" and there were answers at odds with each other.

That is why I am tending to the view that since inertial mass and gravitational mass equals each other and since gravitational mass is not affected by non relativistic speeds, I'm tending to view inertia is more like mass that doesn't change.

So those who say "moving object has more inertia than a stationary one" are wrong and are really talking about momentum.

 

Do you say "a moving object has more inertia than a stationary one"?

Edited May 26, 2015 by Robittybob1

[swansont]

That was what I am trying to get my head around. A month ago I put a question into Google, something like "does inertia increase with velocity?" and there were answers at odds with each other.

That is why I am tending to the view that since inertial mass and gravitational mass equals each other and since gravitational mass is not affected by non relativistic speeds, I'm tending to view inertia is more like mass that doesn't change.

So those who say "moving object has more inertia than a stationary one" are wrong and are really talking about momentum.

 

Do you say "a moving object has more inertia than a stationary one"?

 

I personally don't, because of the ambiguity involved. I speak of momentum, and mass, and kinetic energy. Quantifiable things.

[Robittybob1]

 

I personally don't, because of the ambiguity involved. I speak of momentum, and mass, and kinetic energy. Quantifiable things.

OK but in one of our discussions there was a mass orbiting a central point, when the speed of rotation increases at some point the centripetal force will be exceeded (i.e the string breaks, or the object slips) was that because of the object's increased inertia or increased momentum (or impulse) or something else?

When objects collide they have momentum, energy and there are forces and impulses.

Am I right thinking it all comes down to forces (and mass) and everything results from them?

Edited May 26, 2015 by Robittybob1

[swansont]

OK but in one of our discussions there was a mass orbiting a central point, when the speed of rotation increases at some point the centripetal force will be exceeded (i.e the string breaks, or the object slips) was that because of the object's increased inertia or increased momentum (or impulse) or something else?

When objects collide they have momentum, energy and there are forces and impulses.

Am I right thinking it all comes down to forces (and mass) and everything results from them?

 

Everything in that problem can be discussed without using inertia as a quantifiable term. The principle of inertia — Newton's first law — applies, but you might notice that the word doesn't appear there, either (at least in the ways I've seen it written)

An object moving in a circle must have a force on it equal to mv^2/r. If whatever is exerting a force can't exert that amount, the object will no longer move in a circle.

 

All of motion stems from forces in some way (conceptually; you don;t need a force to have motion, but the fact that F=0 tells you things about the motion). If I were teaching calculus-based physics, I'd start with Newton's laws and work kinematics out from those, rather than how it's normally taught.

[Robittybob1]

 

Everything in that problem can be discussed without using inertia as a quantifiable term. The principle of inertia — Newton's first law — applies, but you might notice that the word doesn't appear there, either (at least in the ways I've seen it written)

An object moving in a circle must have a force on it equal to mv^2/r. If whatever is exerting a force can't exert that amount, the object will no longer move in a circle.

 

All of motion stems from forces in some way (conceptually; you don;t need a force to have motion, but the fact that F=0 tells you things about the motion). If I were teaching calculus-based physics, I'd start with Newton's laws and work kinematics out from those, rather than how it's normally taught.

First Law: https://www.grc.nasa.gov/www/k-12/airplane/newton1g.html

 

Sir Isaac Newton first presented his three laws of motion in the "Principia Mathematica Philosophiae Naturalis" in 1686. His first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is normally taken as the definition of inertia. The key point here is that if there is no net force resulting from unbalanced forces acting on an object (if all the external forces cancel each other out), then the object will maintain a constant velocity. If that velocity is zero, then the object remains at rest. And if an additional external force is applied, the velocity will change because of the force. The amount of the change in velocity is determined by Newton's second law of motion.

can we therefore make Force = ma = mv^2/r?

if v = 2Pi*r/T (the circumference / period

ma = mv^2/r divide both sides by m

a = v^2/r

a = (2*Pi*r/T)^2 / r

a = 4 * Pi^2 * r^2 * T^-2 / r one r cancels out.

a = 4 * Pi^2 * r * T^-2

a = 4 * Pi^2 * r / T^2

a = W^2 * r Omega (angular velocity) squared times radius.

Is that correct? The centripetal acceleration is the angular velocity squared times radius.

[imatfaal]

[latex]v_{tang}=\omega \cdot r[/latex]

 

[latex]a_{centripetal} = \frac{v_{tang}^2}{r}[/latex]

 

[latex]a_{centripetal} = \frac{(\omega\cdot r)^2}{r} = \omega^2 \cdot r[/latex]

[Robittybob1]

....

a = v^2/r

.....

Is that correct? The centripetal acceleration is the angular velocity squared times radius.

I'm just a bit amazed that radial acceleration equals velocity squared divided by the radius. Has that got a similar equation for linear motion?

[latex]v_{tang}=\omega \cdot r[/latex]

 

[latex]a_{centripetal} = \frac{v_{tang}^2}{r}[/latex]

 

[latex]a_{centripetal} = \frac{(\omega\cdot r)^2}{r} = \omega^2 \cdot r[/latex]

Same here has [latex]a_{centripetal} = \frac{v_{tang}^2}{r}[/latex] does this have a linear analog? Well we aren't going to get a radius in linear so my memory just goes blank on this question. Work calls so I can't check it out right now.

Edited May 27, 2015 by Robittybob1

[swansont]

I'm just a bit amazed that radial acceleration equals velocity squared divided by the radius. Has that got a similar equation for linear motion?

Same here has [latex]a_{centripetal} = \frac{v_{tang}^2}{r}[/latex] does this have a linear analog? Well we aren't going to get a radius in linear so my memory just goes blank on this question. Work calls so I can't check it out right now.

 

"Radius" and "linear" really don't mix. One implies a circle, and the other implies "very much not a circle"

 

 

That said, there is an analogue for Newtons laws, as applied to rotation. An object moving in a circle will do so at constant speed unless acted upon by a net torque, and T = I*alpha = dL/dt (alpha is rotational acceleration, L is angular momentum)

[Robittybob1]

With a = 4 * Pi^2 * r / T^2 (a being the centripetal acceleration to keep the acceleration constant (for if it rises things like strings break objects overcome friction or even the rotating mass may even begin to disintegrate) we would have to vary r and T in such a way that the ratio of r/T^2 stayed constant, e.g. if the radius increases there has to be an inverse square drop in the period.

The usual way of exceeding the friction or the tensile strength of the string is to increase the rotational speed or other words decrease the period.

In the case of the ruptured string there will be no more forces and the object till leave at a tangent to the circle it last was travelling. Whereas with the sliding object there will still be frictional forces acting on it till it has reached the edge of what it was on.

So here the friction is doing positive work on the object, and it will accelerate in its tangential speed (decrease the period) and make the tendency to slide even worse.

Edited May 28, 2015 by Robittybob1

[swansont]

The usual way of exceeding the friction or the tensile strength of the string is to increase the rotational speed or other words decrease the period.

 

Yes, eventually the friction cannot supply the force that's required. Then it slides.