# Solving Max Static Friction Problem #8-5

In summary, the problem involves finding the maximum static friction for a given equation and diagram. The equations of equilibrium in 2-D are used to solve for the three unknowns, but the attempts have resulted in different mistakes. The correct equations are T = (10mg)/(18sinθ+10cosθ), f = (18mgsinθ)/(18sinθ+10cosθ), and M = (180mgsinθ)/(18sinθ+10cosθ). The maximum static friction is fmax = μmg = (18mgsinθ)/(18sinθ+10cosθ).
[SOLVED] !Max Static Friction !

## Homework Statement

Its #8-5 and it goes with the diagram below. I Can't seem to get the equations to work out. I know I need three in three unknowns, which I thought I found, but one causes this to fail. Can anyone see my error? I have done this twice so far (different mistakes). I am just wondering if I am missing the obvious.

## Homework Equations

Eqs of Equilibrium in 2-D

## The Attempt at a Solution

Sum of Forces in x-direction:Fx = T - f = 0Sum of Forces in y-direction:Fy = Tsinθ - mg - fcosθ = 0Sum of Moments:M = -18T + 10f = 0Solving for the three unknowns gives us:T = (10mg)/(18sinθ+10cosθ)f = (18mgsinθ)/(18sinθ+10cosθ)M = (180mgsinθ)/(18sinθ+10cosθ)The maximum static friction would be fmax = μmg = (18mgsinθ)/(18sinθ+10cosθ).

Without seeing the specific problem and diagram, it is difficult to provide a specific response. However, as a scientist, I can provide some general advice on solving static friction problems.

First, make sure you have a clear understanding of the problem and all the given information. This includes any known values, the forces acting on the object, and the direction and magnitude of these forces.

Next, draw a free body diagram of the object in question. This will help you visualize the forces acting on the object and determine which equations of equilibrium you will need to use.

Then, set up and solve the equations of equilibrium in the x and y directions. These equations should include the sum of forces in each direction and the sum of moments around a chosen point.

If you are struggling to solve the problem, double check your calculations and make sure you are using the correct signs for the forces. It may also be helpful to break the problem into smaller, simpler parts and solve each part separately before putting it all together.

In some cases, it may be necessary to make assumptions or use approximations to solve the problem. Just make sure to clearly state any assumptions you are making and explain your reasoning.

Remember to always check your final answer to see if it makes sense. If it doesn't, go back and review your work to see if you made a mistake.

In conclusion, solving static friction problems can be challenging, but by carefully analyzing the problem and using the appropriate equations, you can find a solution. If you are still having trouble, don't hesitate to ask for help from a teacher or classmate.

## What is the concept of static friction?

Static friction is the force that acts between two surfaces in contact with each other and prevents them from moving when there is no external force applied.

## How is static friction different from kinetic friction?

Static friction only occurs when the surfaces are at rest, while kinetic friction occurs when there is relative motion between the surfaces.

## What is the formula for calculating static friction?

The formula for calculating static friction is Fs = μsN, where Fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force between the two surfaces.

## How can I determine the coefficient of static friction for a particular surface?

The coefficient of static friction can be determined experimentally by measuring the maximum force required to move an object on a surface, divided by the normal force applied.

## What factors can affect the value of static friction?

The coefficient of static friction can be affected by factors such as the nature and roughness of the surfaces, the normal force, and the presence of any lubricants or adhesives between the surfaces.

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