Coefficients of static and kinetic friction

[hatingphysics]

Suppose that the coefficients of static and kinetic friction have values such that the static coefficient is twice the value of the kinetic coefficient for a crate in contact with a cement floor. Does this mean that the magnitude of the static frictional force acting on the crate at rest would always be twice the magnitude of the kinetic frictional force acting on the moving crate? Give your reasoning.

 

[civil_dude]

Yes, if the coefficients are a ratio of two, so will be the ratio of the forces. F=umg.

 

[kyle8921]

Yes, the magnitude of the static frictional force acting on the crate at rest would always be twice the magnitude of the kinetic frictional force acting on the moving crate. This is because the coefficients of static and kinetic friction are directly related to the force of friction, which is the force that opposes the motion of an object. The static coefficient of friction represents the maximum amount of friction that can be generated between two surfaces when the object is at rest, while the kinetic coefficient of friction represents the amount of friction that is present when the object is in motion.

In this scenario, the fact that the static coefficient is twice the value of the kinetic coefficient means that the maximum amount of friction that can be generated when the object is at rest is twice the amount of friction that is present when the object is in motion. This is due to the fact that when an object is at rest, the force of friction must be equal and opposite to the force applied to the object in order to keep it from moving. Therefore, the maximum amount of friction that can be generated at rest must be greater than the amount of friction present when the object is in motion.

Additionally, the coefficient of friction is a constant value for a given pair of surfaces, regardless of the magnitude of the applied force. This means that even if the force applied to the crate at rest is less than the force applied to the moving crate, the static frictional force will still be twice the magnitude of the kinetic frictional force.

In conclusion, the coefficients of static and kinetic friction have a direct relationship, and the fact that the static coefficient is twice the value of the kinetic coefficient means that the static frictional force will always be twice the magnitude of the kinetic frictional force in this scenario.