Final answer:
The coefficient of static friction (μs) is derived from the maximum static frictional force (fs(max)) before an object starts to move, divided by the product of mass (m) and gravitational acceleration (g), which gives the equation μs = fs(max) / (mg).
Step-by-step explanation:
To derive the coefficient of static friction (μs) in terms of the quantities measured in a typical physics experiment, we start by identifying the relevant force equations and known values. The force of static friction is given by fs = μsN, where N is the normal force and μs is the coefficient of static friction. The normal force, N, is typically equal to the weight of the object, W, when the surface is horizontal, thus N = mg, where m is the mass of the object and g is the acceleration due to gravity.
In experiments, the force of static friction is usually found by gradually applying a horizontal force to an object until it starts to move. At the threshold of movement, the applied force is equal to the maximum static frictional force. The equation for static friction becomes fs(max) = μsN = μs(mg), from which we can solve for μs by measuring the applied force (fs(max)) and knowing the mass of the object and the acceleration due to gravity.
This means that μs = fs(max) / (mg). To determine μs, one would measure the maximum force needed to initiate movement, along with the mass of the object, to calculate the coefficient of static friction.