# Relationship between force and coefficient of friction

### Coefficient of friction - Simple English Wikipedia, the free encyclopedia

Relationship between force of friction, T, and horizontal displacement, l, obtained from test measuring coefficient of friction between steel ball and steel plate. The frictional force is also presumed to be proportional to the coefficient of friction . Typically there is a significant difference between the coefficients of static. The standard friction equation shows the relationship between the resistive force of friction, the coefficient of friction and the normal force.

## Coefficient of friction

For example, a person sliding into second base during a baseball game is using the force of kinetic friction to slow down. If there were no kinetic friction, the baseball player would just continue sliding yes, this would make stealing bases in baseball difficult. But if you were to zoom in, you would see that the surfaces are rough at a microscopic level. For instance, the surfaces of the box and floor as shown below are actually rough and jagged at a microscopic level.

Openstax College Physics Friction arises in part because of the roughness of the surfaces in contact, as seen in the expanded view. In order for the object to move, it must rise to where the peaks can skip along the bottom surface. Thus a force is required just to set the object in motion.

### Find friction force, given mass and coefficient of friction - Text TutoringText Tutoring

Some of the peaks will be broken off, also requiring a force to maintain motion. Much of the friction is actually due to attractive forces between molecules making up the two objects, so that even perfectly smooth surfaces are not friction-free.

Such adhesive forces also depend on the substances the surfaces are made of, explaining, for example, why rubber-soled shoes slip less than those with leather soles. But to be completely honest, we still don't have a complete understanding of the microscopic causes of friction. Because there is no acceleration, any coordinate system is fine - a system parallel and perpendicular to the ramp is pretty convenient, though, because two of the forces are along those directions.

Applying Newton's second law to the forces in the y-direction: Again, we can use this equation to solve for the normal force: Applying Newton's second law in the x-direction gives: The box is moving at a constant velocity, so that means the acceleration is zero. Solving for the kinetic force of friction gives: The coefficient of kinetic friction can be found from the normal force and the frictional force: This is actually a relatively large value for the coefficient, so it's not easy to move this box along this ramp.

**Kinetic Friction and Static Friction Physics Problems, Forces, Free Body Diagrams, Newton's Laws**

Example 2 Consider another example involving an inclined plane, only this time there will be two boxes involved. This is quite a challenging example, so don't be too intimidated if it looks tricky. Start by seeing if you agree with the free-body diagrams; if you understand those, you've made an important step in learning some physics. Box 1, a wooden box, has a mass of 8.

### Standard Friction Equation by Ron Kurtus - Physics Lessons: School for Champions

Box 2, a cardboard box, sits on top of box 1. It has a mass of 1.

The coefficient of kinetic friction between the two boxes is 0. The two boxes are linked by a rope which passes over a pulley at the top of the incline, as shown in the diagram. The inclined plane is at an angle of What is the acceleration of each box? The diagram for the situation looks like this: The next step is to draw a free-body diagram of each box in turn.

## Standard Friction Equation

To draw these, it helps to think about which way the boxes will accelerate. The two boxes are tied together, and the heavier box will win The pulley, by the way, simply changes the direction of the tension force.

We're assuming that the pulley is massless and frictionless, so both boxes feel the same tension force. It's important to know the direction of the acceleration or, if you don't know, to guess and apply what you figured out or your guess consistently to both boxes. The free-body diagram of box 1 is relatively complicated, with a total of 6 forces appearing.

The free-body diagram for box 2 is a little easier to deal with, having 4 forces, so that's a good place to start. For box 2 - start by summing the forces in the y-direction, where there is no acceleration: This can be solved to give the normal force: Now find the net force in the x direction, where there is an acceleration up the slope: There are two unknowns in this equation, the tension T and ax, the acceleration.

We can at least solve for T in terms of ax, like this: Now move on to box 1.