Both words originate from “Force”.  However they change their meaning when adding “ful” or “ible” as a suffix.

The adjective forcible means done by force or involving the use of physical force or violence. It also means to force someone to do something.   Forcible means to be forced to do something against one’s will.  Forcible came into use in the early 1500s from the Old French forcier, meaning to conquer by violence.

Examples:

• The raid on the terrorists required a forcible entry into their hideout.
• The thieves made a forcible entry into the house by breaking the window.The man wielding a gun was forcibly removed from the aircraft before takeoff.
• A woman was forcibly raped at gun point.
• During the Mughal rule in India, many people were forcibly converted to Islam.
• Lara was forcibly fed with a bitter medicine, which made her cry.
• Since Bill refused to get up from his seat, he was forcibly removed from it.
• Despite many protests, the demolition squad forcibly broke down the building.
• Forcible measures were taken, to make the residents vacate an illegal building.
• The landlord threatened the tenant with forcible eviction if the rent was not paid immediately.
• The forcible suppression of all opposition is the guiding principle of governments in some countries.
• From time to time emigration takes the shape of a mass movement, which the government stops by forcible measures.
• The police forcibly broke open the door but found no one was inside.

In general, forcible describes the use of power.

Forceful describes a person or thing that is powerful, assertive, and effective. Forceful is an adjective which may describe a person or argument, among other things.  An orator or a speaker may be forceful in conveying his ideas; advertising may be forceful in influencing people to buy certain goods; a book may be forceful in opening your mind to matters which you never thought of before; the media is forceful in opening our eyes to the refugee crisis in Europe.

More examples:

• In his successive offices Mr Roosevelt, by reason of his forceful personality, achieved a national prominence out of ordinary proportion to the importance of his official position.
• The lawyer’s arguments were so forceful that the jury reached a verdict of “not guilty”.
• The winds in the vicinity of the volcano are not quite as forceful as they have been, so the ash plume is higher closer to the volcano. 
• Mahatma Gandhi’s peaceful but forceful demonstrations won India its freedom.
• The forceful nature of the earthquake devastated Nepal.
• His forceful arguments against religious persecution resulted in an anti-Islam bill not being passed.
• Donald Trump’s oratory is forceful, but will he win the nomination?
• The CEO of the company was forceful in his speech demanding more productivity from his staff.
• Denied the cup last year, the team has re-emerged as a more forceful unit.
• Not being the most assertive or forceful of people I take criticism too personally and can get quite upset.
• The book makes a forceful argument that not every form of pleasure is desirable nor is every means of achieving happiness acceptable.
• To help the economy to recover, the government must implement forceful measures to curb spending.
• The social worker spoke forcefully about the need to educate the girl child.
• From the above examples both words convey using force, but forcible is used more for exerting physical power and forceful for effectively conveying one’s ideas.

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