Final answer:
The necessary coefficient of static friction to keep a block from moving is dependent on the forces acting upon the block and can be calculated using the equation for static friction, considering the object's weight and the normal force.
Step-by-step explanation:
The coefficient of static friction (μₛ) required to keep a block from moving depends on the other forces acting on the block. To determine this, we need to know the force necessary to cause movement and the force of static friction that can be provided by the surface. This is calculated using the equation for static friction, Fₛ = μₛs N, where μₛs is the coefficient of static friction and N is the normal force (the force perpendicular to the surface). The coefficient needed will be the one that provides a force equal to or greater than the external force attempting to move the block.
In scenarios provided in the question prompts like the block connected to a spring or a crate on a floor with known values of static friction, we calculate the force needed using the spring constant and mass or the weight of the crate as related to gravity and compare it to the product of the coefficient of static friction and the normal force. The correct coefficient would prevent the object from moving by equating to or exceeding necessary counteracting force.