In the discussion of ordinary care the most important concept is what is the source of that duty. That is,the source of the duty to exercise ordinary care. In terms of a tort that source of duty to exercise ordinary care cannot be a contract. If the source of the duty is a contract then what you have is a breach of contract claim. A tort claim is different. Tort damages likewise are different than contract damages.The duty to exercise ordinary care may arise from the rules of the road in regards to a automobile collision.In regards to a slip and fall accident the source of the duty may be the state code known as the Property Maintenance Code. That Code may establish certain standards as to how property is to be maintained.In the case of a medical procedure the source of the duty may be publications put out by professional associations that tell surgeons how particular procedures are to be performed. Likewise in regard to the manufacture of products there may be industry standards as to how particular products are to be manufactured.
The establishment of what constitutes ordinary care is only part of the battle in a tort claim. In addition there must be proof that the party charged with the wrongdoing actually violated that standard of ordinary care.
For more information on these issues and other injury related concepts see the other pages on this site and also see the pages on Wikipedia.