A dimensionless physical quantity the specifies the interaction of two object is called coefficients.
The value coefficient of kinetic friction is changes depending on the nature of the material used. Generally, the coefficients give the ratio of two quantities involved in the action. In this post, let us discuss how to find coefficient kinetic friction and its consequences.
How to find coefficient of kinetic friction
Let us consider two surfaces, such that one surface is moving in contact with another one. The friction always resists the movement and finally stops the motion of the surface in the opposite direction of the motion.
A general formula to find the coefficient friction is given by the ratio of friction force and the normal reaction acting on the surfaces in a perpendicular direction.
On rearranging the above expression, we can find out the kinetic friction as well.
How to calculate uncertainty of coefficient of kinetic friction
The uncertainty occurs due to the misalignment of the coordinate axes along the direction of the motion. Along with the normal force, the tangential force is acting on the system. This tangential force gives an account for the occurrence of uncertainty of the coefficient of the kinetic friction.
The value of the coefficient is not measured directly through the experiment. It is determined by calculating all the forces acting on the system and the angle of inclination of the object with the surface.
The general expression for the coefficient of kinetic friction is given by
Let us consider the sliding of an object in a plane. The sliding of the object is taken for the various angle of the object along the plane for different instances. Then calculate the coefficient of kinetic friction for all the angles.
The above statement tells that the value of coefficient of kinetic friction changes with change in the angle. This deviation is due to the uncertainty of kinetic friction coefficient. Let us study how to find the coefficient of kinetic friction with uncertainty.
Along with the normal force FN, the tangential force also contributes to the evolution of friction force. This leads to an error in calculating the coefficient of kinetic friction. The uncertainty measurement compensates for the error that occurred during the calculation.
The normal force is acting along the Y-axis, and the angle of misalignment be β. And the tangential force is acting along the X-axis with the misaligned angle of α. These normal and tangential forces are in contact, and the resultant force along the X and Y axes are given by
FX = FF cosα + FN sinα
FX = µK FN cosα + FN sinα
FX = FN (µK cosα + sinα)
Similarly for Y axis
FY = FN cosβ – FF sin β
FY = FN (cosβ – µK sinβ) By solving the resultant forces, the uncertainty in the friction is given as
In order to calculate the combined standard uncertainty measurement, the standard uncertainty function must be a standard value of input values and the partial derivatives of the frictional coefficient. The law of “propagation of uncertainty” helps us to give a standard value for the uncertainty in the friction. It is given by the equation.
Where, u is the uncertainty of the given system.
On differentiating the individual variables, we get the standard value of uncertainty in the coefficient of kinetic friction.
This gives the standard uncertainty value for the input forces acting on the system. By substituting these values in the partial derivative equation, we get the uncertainty value.
How to calculate coefficient of kinetic friction without mass
To calculate the coefficient of kinetic friction without mass, let us consider a block moving on a flat surface. The block of mass “m” moving with acceleration “a” in the direction of the applied force. The normal force acting between the block and the surface be FN which is perpendicular to the motion of the block. We know that the friction force acting between the block and surface to retard the motion is given by the equation,
FK = µK FN
According to Newton’s second law of motion, the force acting on the moving body equals mass times the acceleration.
F = m* a
The normal force is influenced by the force of gravity given as
FN = m*g
Substituting in the equation of frictional force, we get
FK = µK m*g
Since the body is moving and the force acting on the block is kinetic friction force, Newton’s law can be modified as
FK = m* a
On equating the above two equations we get,
µK m*g = m* a
µK g = a Rearranging the equation we get,
This gives the value of the coefficient of kinetic friction.
Frequently Asked Questions
Does the calculation of kinetic friction without mass give the same value of coefficient obtained by considering the mass?
Yes, the value of the coefficient of kinetic friction with or without considering the mass is the same.
Since friction is a quantity that is independent of the absolute mass of the system, the mass does not affect the value of the friction involved in the process. Hence the coefficient of kinetic friction remains unchanged with or without considering the mass of the object.
Does the nature of the material influence the coefficient of kinetic friction?
The coefficient of kinetic friction is a numerical value that gives the evidence for the presence of friction force between the objects.
Since friction is influenced by the nature of the material, it is so evident that its coefficient is also largely influenced by the nature of the material.
What is necessary to find the coefficient of kinetic friction of a moving object?
Without the coefficient of kinetic friction, it is quite difficult to measure the force that makes the object to hinders its motion.
The friction is always proportional to the normal perpendicular reaction between the surfaces. This proportionality relation is specified by the dimensionless quantity called the coefficient. The coefficient of kinetic friction measures the absolute value of the friction force that stops the moving object.
Can the value of the coefficient of kinetic friction be greater than 1?
Generally, the value of the kinetic friction coefficient ranges from 0 to 1. Sometimes it gives a value of coefficient exceeds 1.
If the influence of friction force is stronger than the perpendicular reaction between the two moving surfaces, the value of kinetic friction coefficient exhibit the value greater than 1. Maximum frictional force makes the object to restrict its motion so that automatically the coefficient of kinetic friction increases proportionally.
Does greater coefficient of kinetic friction lead to energy dissipation?
The dissipation of energy due to friction can be described in terms of energy conservation Law.
A greater coefficient of kinetic friction means the friction force is stronger than the applied force. The challenging task is to keep the body in motion in the presence of friction. Hence it takes much force to keep the body in motion. The maximum force exerted to keep the body in motion causes the kinetic energy dissipation released in the form of heat.