Full size image. For the friction coefficient, we Lesbian grandams get At high frequencies, the plateau value of will be achieved. Introduction If you've ever been shot with a rubber band then you know it has energy in it—enough energy to smack you in the arm and cause a sting! Surface roughness can become significant if the roughness is very high. Note that the main logic of the result 23 is not dependent on the details of the model and even on it dimensionality. The roughness is assumed to be randomly self-affine with a Rubber band friction exponent H in the range from 0 to 1. Since the kinetic energy of the car is converted to friction energy Rubber band friction - we have the expression. Mindlin, R.
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Underwater work. Already a subscriber? Miss nude san francisco, fly wheels. These are all challenges you can overcome with fiction little engineering effort! Specifically it stores elastic potential energy—the type of energy stored when a material is deformed as Rubber band friction to gravitational potential energy, the type Rubber band friction get when you raise an object off the ground. Create a frame that's 2 craft sticks long as shown picture 1. In animal husbandryrubber bands are used for docking and castration of livestock. Aquathlon underwater wrestling Apnoea finswimming Freediving Underwater ice hockey. When we did this study mentioned above, we identified the following dissipation mechanism. This article needs additional citations for verification. When a rubber block is sliding on a hard rough substrate the surface asperities of the substrate will exert fluctuating forces on the rubber surface which, because of the internal friction of the rubber, will result in energy transfer from the translational motion of the block into the irregular thermal motion see FIGURE below. Total Rubber Friction. Underwater photography sport. Consider a rubber block in relative motion with a hard, randomly rough substrate. At a particular magnification frictio effect brakes down due to high temperatures and stresses prevailing in the contacting regions.
Key concepts Physics Mathematics Energy Projectiles.
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- Contact mechanics and friction are both topics of huge importance with many applications in Nature and technology.
- A rubber band also known as an elastic band , gum band or lacky band is a loop of rubber, usually ring shaped, and commonly used to hold multiple objects together.
- Did you ever suspect that rubber bands could also be a fun way to learn about physics and engineering?
- Rubber bands are a convenient and effective way to teach energy transformation, and this rubber band car makes that lesson a blast!
Key concepts Physics Mathematics Energy Projectiles. Introduction If you've ever been shot with a rubber band then you know it has energy in it—enough energy to smack you in the arm and cause a sting! But have you ever wondered what the relationship is between a stretched rubber band at rest and the energy it holds? The energy the rubber band has stored is related to the distance the rubber band will fly after being released.
So can you guess one way to test how much energy a stretched rubber band contains? Background No mechanical contraption would be any fun if it did not work.
But "work," in the physics sense, takes energy. Consider a rope and pulley that bring a bucket up a well. The energy that makes this mechanical system work is provided by a person who pulls up the rope. There are actually two different kinds of energy: potential energy, which is stored energy, and kinetic energy, which is energy in motion. A great example of the difference between kinetic and potential energy is from the classic "snake-in-a-can" prank. This is an old joke where you give someone a can of peanuts and tell them to open it, but inside is actually a long spring that pops out when the lid is twisted off.
Because the spring is usually decorated to look like a snake, this prank usually causes the victim to jump back and shout in surprise! When the snaky spring is compressed and secured inside the unopened can, it has potential energy. But when the can is opened, the potential energy quickly converts to kinetic energy as the fake snake jumps out.
You will want a place with a lot of clearance that has a concrete or other hard surface on which you can draw with chalk. If necessary, have an adult do the rubber band launching.
With your chalk, draw a line in front of your toes. This is where you will line your feet up when you shoot your rubber bands. This is also the mark from where you will measure the distances your rubber bands have flown. Make sure he or she has a piece of chalk. Remember the angle and height at which you hold the ruler because you will need to keep it the same for each rubber band launch.
Have your helper circle where each lands. Write these distances down under the heading "10 cm. Shoot at least five rubber bands for each stretch length.
After each launch, have your helper circle where they land. After launching five rubber bands at a given stretch length, measure the distances from your line to the circles. Write these distances under a heading for their stretch length for example, "20 cm". Did they land far from where the rubber bands landed that were launched using different stretch lengths? Do your data follow any type of pattern or trend? What was the relationship between the stretch length and the launch distance?
What do you think this indicates about the relationship between potential and kinetic energy when using rubber bands? How do these variables affect the distance the rubber band travels?
Design a separate activity to test each of these variables separately. How do the data collected using these other mechanical systems compare with that collected using rubber bands?
Can you define an equation that expresses the relationship between potential and kinetic energy in this system? Observations and results Did the rubber bands stretched to 30 cm launch farther than the other rubber bands? Did you see a linear relationship between the launch distance and stretch length when you graphed your data? You input potential stored energy into the rubber band system when you stretched the rubber band back.
Because it is an elastic system, this kind of potential energy is specifically called elastic potential energy. When the rubber band is released, the potential energy is quickly converted to kinetic motion energy. This is equal to one half the mass of the rubber band multiplied by its velocity in meters per second squared. Using these equations, you can calculate the velocity of the rubber band right when it is released, and find that the velocity has a linear relationship with the stretch length.
Because the amount of time that the rubber band spends in the air is dependent on its initial height and force of gravity, and these factors should not change between your trials, then how far the rubber band flies depends on its initial velocity. Consequently, after you graph your data, you should see a roughly linear relationship between the stretch length and the launch distance.
More to explore What Is Energy? You have free article s left. Already a subscriber? Sign in. See Subscription Options. Key concepts Physics Mathematics Energy Projectiles Introduction If you've ever been shot with a rubber band then you know it has energy in it—enough energy to smack you in the arm and cause a sting!
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Asked in Brakes and Tires What causes car tires to leave skid marks on the pavement? Check out my work: www. Marx Charles T. This article needs additional citations for verification. Breathing performance of regulators Porpoise regulator Single-hose regulator Twin-hose regulator. In case you want to learn more about the validation of the theory please visit our validation section. More by the author:.
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Sliding and Friction: Weekly Science Activity | Science Buddies Blog
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The resulting frictional force as a function of velocity shows the same qualitative behavior as in the case of planar surfaces: it increases monotonically before reaching a plateau. However, the dependencies on normal force, sliding velocity, shear modulus, viscosity, rms roughness, rms surface gradient and the Hurst exponent are different for different macroscopic shapes.
We suggest analytical relations describing the coefficient of friction in a wide range of loading conditions and suggest a master curve procedure for the dependence on the normal force.
Experimental investigation of friction between a steel ball and a polyurethane rubber for different velocities and normal forces confirms the proposed master curve procedure. Friction is a phenomenon that people have been interested in for thousands of years but its physical reasons are not clarified completely yet. Not only is it still not possible to predict the frictional force theoretically, there are also no reliable empirical laws of friction which would satisfy the needs of modern technology.
According to Amontons, the coefficient of friction does not depend on the normal force and the contact area. However, already Coulomb knew that the coefficient of friction, even between the same material pairing, can change by a factor of about four depending on the contact size 2 and on the normal force 2.
As a matter of fact, there are no obvious reasons for the validity of Amontons' law. On the contrary, much effort has been made in the th—60th years to understand why Amontons' law is approximately valid 3 , 4. Several recent studies focused on violations of Amontons' law for static friction due to the dynamics of onset of sliding, which have been studied both experimentally 5 , 6 , 7 and theoretically in three-dimensional 8 and one-dimensional models 9 , The detailed dependence of the sliding coefficient of friction on normal force was not studied yet.
In the present paper, we investigate the force of sliding friction beyond Amonton's law for elastomers with linear elastic rheology, and formulate rules for constructing generalized laws of friction for this class of materials.
Theoretical findings are supported by experimental data. We use the standard assumption that elastomer friction is caused by energy dissipation in the volume of the elastomer due to local deformations 11 , For illustrations and basic understanding we implement this mechanism in the frame of a one-dimensional model based on the method of dimensionality reduction MDR As this method has recently been subject of a very controversial discussion, we would like to briefly describe the arguments for and against its validity.
For small normal or tangential movements of three-dimensional bodies in contact, the total energy dissipation can be calculated either by integrating the dissipation rate density over the whole volume or equivalently determined over total force and displacement.
Either method, providing the correct relation between macroscopic forces and displacements is therefore suited for simulation of elastomer friction. It was shown that the force-displacement relation of elastic bodies can be described by a contact with a properly defined one-dimensional foundation, provided the indenter is an arbitrary body of revolution Furthermore, the applicability of the method of dimensionality reduction MDR again with respect to the force-displacement relations was later extended and verified for contacts of randomly rough, self-affine surfaces with elastic 14 and viscous 15 media and for tangential contacts In the paper by Lyashenko et.
The authors of this paper showed that the MDR does not allow the simulation of the real contact area of random surfaces apart from the limit of very small forces. This conclusion is correct and is confirmed by Popov in the review paper 18 and the monograph 16 devoted to the MDR. The force-displacement relations, on the contrary, are correctly described in the frame of the MDR. This shows, that the MDR can be a useful modeling tool even for simulation of fractal rough surfaces as long as we stay within the standard Grosch' paradigm of the rheological nature of elastomer friction Following the above arguments, we use the MDR as a basis for the simulations of elastomer friction in this paper.
In the subsequent sections, the restrictions are discussed and the model is generalized for arbitrary linear rheology. Let us consider a rigid indenter having the form consisting of the macroscopic power-shaped profile and a superimposed roughness h x , as shown in Figure 1.
Throughout this paper, we will assume that the indentation depth of the indenter, d , is much larger than the rms value of the roughness,. This means that the large-scale configuration of the contact is primarily determined by the macroscopic form of the indenter and does not depend on the roughness Figure 2a.
The normal force in each particular element of the viscoelastic foundation is given by where u is the vertical displacement of the element of the viscoelastic foundation. For elements in contact with the rigid surface, this means that The normal and the tangential force are determined through equations We first consider the force of friction at very low velocities.
The contact configuration is then approximately equal to the static contact. This equation shows, that both the macroscopic shape of the indenter and the microscopic properties of surface topography determine the coefficient of friction: the contact length is primarily determined by the macroscopic properties shape of the body and the normal force while the rms gradient is primarily determined by the roughness at the smallest scale.
Consider the opposite case of high sliding velocities. The detachment of the elastomer from the indenter occurs when the normal force which is the sum of elastic and viscous force, Eq. If the rms value of the elastic force and the viscous force become of the same order of magnitude, the detachment will occur in almost all points with negative surface gradient, thus a one-sided detachment of the elastomer from the indenter will take place.
Characteristic rms values of the three terms in Eq. For the normalized coefficient of friction we get For an exponential probability distribution function of the gradient of the surface, the ratio of the integrals in 15 is equal to , in accordance with 14 , and it depends only weakly on the form of the distribution function.
The validity of equation 17 was numerically confirmed for the following ranges of parameters. All values shown below were obtained by averaging over realizations of the rough surface for each set of parameters.
All data collapse to one master curve described by equation At low frequencies, the shear modulus tends towards its static value G 0. For simplicity, we will assume that the macroscopic contact mechanics of the indenter is completely governed by the static shear modulus G 0 , which is correct for sufficiently small sliding velocities.
On the other hand, the frictional force is almost completely determined by the smallest wavelength components in the spectrum of roughness and thus by high frequency rheology. For the friction coefficient, we therefore get At high frequencies, the plateau value of will be achieved.
This equation shows that the coefficient of friction for rigid bodies having macroscopic power-law shape has the general form where p v is a function of velocity, which depends on the rheological properties of the elastomer.
Following this hypothesis, we assume that at different velocities, the measured curves are only shifted pieces of the same curve. The resulting curve gives the dependence of the coefficient of friction in a wider range of forces than the range used in the experiment. At the same time, the shift factors at different velocities will provide the dependence of the coefficient of friction on velocity.
The result is a complete dependence of the coefficient of friction in a wide range of velocities and forces.
Repeated for different temperatures and using the standard master curve procedure 12 , this will lead to restoring the complete law of friction as function of velocity, temperature and normal force. However, in the present paper, we avoid the well discussed subject of the temperature dependence and concentrate our efforts completely on the force dependence. Note that the main logic of the result 23 is not dependent on the details of the model and even on it dimensionality.
The scaling relation 23 follows solely from the assumption that the macroscopic form of the contact is determined by the macroscopic properties of material and do not depend on microscopic details, and on the other hand, that the microscopic properties are determined mainly by the indentation depth.
These general assumptions are equally valid for one-, two- and three dimensional models. Below we explain this important point in more detail. It is well known, that if a rigid body of an arbitrary shape is pressed against a homogeneous elastic half-space then the resulting contact configuration is only a function of the indentation depth d.
At a given indentation depth, the contact configuration does not depend on the elastic properties of the medium, and it will be the same even for indentation of a viscous fluid or of any linearly viscoelastic material.
This general behavior was recognized by Lee and Radok 22 , 23 and was verified numerically for fractal rough surfaces Further, the contact configuration at a given depth remains approximately invariant for media with thin coatings 24 or for multi-layered systems, provided the difference of elastic properties of the different layers is not too large It was argued that this is equally valid for media which are heterogeneous in the lateral direction along the contact plane Along with the contact configuration, all contact properties including the real contact area, the contact length, the contact stiffness, as well as the rms value of the surface gradient in the contact area will be unambiguous functions of the indentation depth.
Note, that this is equally valid for tangential contact. This result does not depend on the form of the body and is valid for arbitrary bodies of revolution 29 and even for randomly rough fractal surfaces This fact, that the contact configuration is solely determined by the indentation depth is as a matter of fact the only physical reason needed to get the simple scaling relations for the coefficient of friction between rough rigid bodies and linearly viscoelastic elastomers described by equation While the particular form 22 can depend on the model used, the general functional form 23 is a universal one and is not connected with the method of dimensionality reduction used in this paper.
Our numerical and theoretical analysis shows that under some conditions the dependencies of the coefficient of friction on the normal force, presented in double logarithmic axes, is self-similar at different velocities and can be mapped onto each other by a simple shifting along the force axis. The measured coefficients of friction as a function of force are shown in Figure 5. If the shifting procedure formulated in last Section is valid, all the curves shown in this figure have to be considered as different parts of the same curve shifted along the log F N -axis.
It is interesting to note that the resulting master curve has two distinct linear regions, meaning a power dependence of the coefficient of friction on the normal force.
Figure 7 shows the dependence of the shifting factor on the sliding velocity. This result can be interpreted as follows. This is compatible both with the rheological data for the used rubber compound and with data from literature. We analyzed the frictional behavior of elastomers under the following simplifying assumptions: a the rigid counter body has a power law shape e. Under these assumptions, we have shown that the coefficient of friction is a function of a dimensionless argument, which is a multiplicative function of powers of velocity and force.
The exact form of this argument depends both on the rheology and the macroscopic form of the indenter. We have proven this procedure with experimental results obtained on polyurethane rubber. In combination with the widely used shifting procedure for varying temperature 12 , it allows to determine generalized laws of friction as functions of velocity, temperature and normal force.
The results of the present paper generalize and validate the results of the pioneering work by Schallamach Method of Dimensionality Reduction MDR is based on mapping of three-dimensional contact problem to contacts with one-dimensional elastic or viscoelstic foundations It gives exact solutions for contacts of bodies of revolution, and provides a good approximation for all properties which depend on the force-displacement relationship such as contact stiffness, electrical resistance and thermal conductivity, and also dissipated energy and frictional force for elastomers.
The details are described in the introduction and at the beginning of the Section Results. The experimental set-up for measuring elastomer friction is shown in Figure 8. The maximum pressure in the contact area was, in all experiments, at least one order of magnitude smaller than the latter, so that there was no plastic deformation of rubber.
Under these conditions the dynamic friction coefficient was measured at constant normal force and horizontal velocity. A total of measurements were taken. Data for any parameter set normal force and temperature was averaged over six measurements. Every measurement series was started at the smallest normal force, and increased in steps. At every level of normal force, the measurement was made with 28 horizontal velocities.