Final answer:
The element associated with skin and hair coat is the protein keratin, which provides strength to hair and nails and serves several biological, social, and protective functions.
Step-by-step explanation:
The element most associated with skin and hair coat in mammals is keratin, which is a tough protein. This protein forms fibers that make hair and nails strong and resistant. The hair shaft consists of dead, keratin-filled cells that overlap each other, aiding in water repellence, much like roof shingles. Apart from providing strength, hair serves several homeostatic functions such as protecting against UV radiation, acting as a sensory input, and aiding in temperature regulation. Similarly, nails, made from dead keratinized cells, protect our extremities and enhance the sense of touch. Human hair also has social and cultural significance, indicative of various traits like age, biological sex, and group affiliation.