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Static friction is the force that prevents an object from moving when it is at rest, even when a force is applied. Imagine trying to push a book on a table. Initially, it does not move no matter how much effort you seem to exert. That is the static friction at work. Static friction acts to stop motion until a certain threshold, called the maximum static friction, is surpassed by an applied force. Without static friction, objects would slide off surfaces far too easily. It acts as the adhesive force between the contact surfaces of the book and the table. In our exercise, a force of 2.25 N is needed to overcome this static grip between the stationary book and the table.

When calculating the coefficient of static friction, ( \( \mu_s \)) ), you can use the formula:\[ f_s = \mu_s \cdot N \] where:

• \( f_s \) is the force of static friction, here 2.25 N.
• \( \mu_s \) is the coefficient we aim to find.
• \( N \) is the normal force exerted by the object onto the surface, calculated as mass times gravity (\( N = m \cdot g \)).

In this example, the book has a normal force of approximately 17.64 N, leading us to find a coefficient of static friction of around 0.128.

Kinetic friction comes into play once the object has started moving. Unlike static friction, it is concerned with objects already in motion. It is this force that acts opposite to the direction of motion, slowing it down or keeping it at a steady speed against an externally applied force. Once the book on the table is sliding, it requires less force to keep it moving compared to what was needed to start it moving. This ongoing resistance is due to kinetic friction and acts parallel to the surface.

In the exercise,when the book slides over the tabletop, only a force of 1.50 N is needed to maintain its constant speed. This shows that the maximum static friction has been overcome, and kinetic friction works to ensure the slide does not pick up speed unrestricted by other forces. The formula to find the coefficient of kinetic friction, ( \( \mu_k \)) ), is given by:\[ f_k = \mu_k \cdot N \] where:

• \( f_k \) is the kinetic friction force, noted here as 1.50 N.
• \( \mu_k \) is what we calculate.
• \( N \) is, again, the normal force of about 17.64 N.

The resulting calculation provides a kinetic friction coefficient of about 0.085, indicating how much easier it is to keep moving rather than start moving the book.

The coefficient of friction is an important parameter in physics that lets us quantify how much friction exists between two surfaces. It is a dimensionless value, indicating the degree of resistance to movement that the surfaces exert against each other. There are separate coefficients for static (\( \mu_s \)) and kinetic (\( \mu_k \)) friction since the resistance encountered by an object in motion differs from when it is stationary. Understanding these coefficients helps in predicting the force needed to move an object or keep it moving, which is vital in many practical and everyday applications.

• The higher the coefficient, the more grip or friction present.
• A lower coefficient points to smoother, easier sliding surfaces.

In the exercise, using our calculated values:

• \( \mu_s \approx 0.128 \) for static friction indicates the level of resistance before movement begins.
• \( \mu_k \approx 0.085 \) for kinetic friction shows resistance during the sliding motion.

These coefficients help engineers in designing materials and surfaces, to either maximize grip or minimize friction, depending on the intended use.