Yes, it is possible for two different materials to have the same coefficient of friction but require different applied forces to start sliding them on each other. This can be understood by considering the concept of static friction and the factors that influence it.
The coefficient of friction (μ) is a dimensionless value that represents the ratio of the force of friction (F_friction) between two surfaces to the normal force (F_normal) pressing the surfaces together. It is often divided into two types: static friction (μ_s) and kinetic friction (μ_k).
Static friction comes into play when an object is at rest and prevents it from moving when an external force is applied. Kinetic friction, on the other hand, occurs when an object is already in motion.
When we talk about the coefficient of friction being the same for two different materials, we usually refer to the kinetic friction coefficient (μ_k). This means that once the objects start sliding, the resistance to motion provided by the friction force is similar for both materials.
However, the static friction coefficient (μ_s) can vary between different materials. Static friction is typically greater than kinetic friction, meaning it requires more force to overcome static friction and initiate motion compared to the force needed to maintain the sliding motion (kinetic friction).
So, even if two materials have the same coefficient of kinetic friction, their static friction coefficients can differ. This difference can result in different forces needed to overcome static friction and initiate sliding. The variation in the microscopic properties, surface roughness, intermolecular interactions, and other factors specific to each material can affect the static friction coefficient and the force required to start the motion.
In summary, the coefficient of friction may be the same for two materials in terms of their kinetic friction, but differences in their static friction coefficients can lead to varying forces required to initiate sliding.