The adjective forceful means full of force: powerful, vigorous, confident, assertive. (Noun: forcefulness. Adverb: forcefully.)

The adjective forcible means done by force or involving the use of physical force or violence. Forcible can also mean effective or convincing. (Noun: forcibleness. Adverb: forcibly.)

Also see the usage notes below.

Examples:

• "When we say that someone has a strong or forceful personality, we mean that he or she has a commanding presence that causes others to pay attention to and defer to them."
  (Les Carter, Enough About You, Let's Talk About Me, 2005)

• "Brave New World makes a forceful argument that even if happiness is a legitimate goal of public policy, not every form of pleasure is desirable, nor is every means of achieving universal happiness acceptable."
  (Derek Bok, The Politics of Happiness, 2010)
• Forcible entry is often required in emergencies where time is a critical factor.
• "[T]he report contained harrowing evidence, finding that forcible removal of indigenous children was a gross violation of human rights that continued well after Australia had undertaken international human rights commitments."
  (Damien Short, Reconciliation and Colonial Power: Indigenous Rights in Australia, 2008)

Usage Notes:

• "Forceful, forcible, and forced have distinct, if related, meanings. Forceful is used to describe something that suggests strength or force: a forceful argument. Forceful measures may or may not involve the use of actual physical force. Forcible is most often used concerning actions accomplished by the application of physical force: There had clearly been a forcible entry into the storeroom. The suspect had to be forcibly restrained.
  
  "Forced is used to describe a condition brought about by control of an outside influence: Products made by forced labor are generally shunned in the international marketplace. It became necessary for the pilot to make a forced landing. Her displeasure was evident in her forced smile."
  (Webster's New Essential Writer's Companion. Houghton Mifflin, 2007)

• "A forceful (not forcible) person is vigorous or strong or powerful; 'acting with force, impetuous, violent' is forceful; a writer, a painter, an orator that produces a powerful effect is forcible; a cogent or expressive speech or style is either forceful or forcible; a weapon drawn with force or violence is a forceful weapon; something done by force, or involving the use of force or violence, is forcible (e.g. 'a forcible expulsion,' 'forcible means'), esp. in law, as in forcible detainer, forcible entry, forcible abduction, forcible dissolution (of, e.g. Parliament) (OED)."
  (Eric Partridge, Usage and Abusage: A Guide to Good English, revised by Janet Whitcut. Norton, 1997)

Practice:

(a) "In the early years, the colony needed a man of _____ character to bang it into shape, but Stuyvesant was too proud, irascible and stubborn to know when it was time for him to step down."
(Stephen R. Bown, Merchant Kings: When Companies Ruled the World, 1600-1900, 2009)

(b) "Held in captivity, under _____ restraint if necessary, indentured servants were treated as inferiors and faced severe punishment if they resisted authority."
(Scott Christianson, With Liberty for Some: 500 Years of Imprisonment in America, 1998)

Answers to Practice Exercises

Glossary of Usage: Index of Commonly Confused Words

200 Homonyms, Homophones, and Homographs