exertion, endeavour, encourage, strive, make effort, diligent
勉 centers on sustained effort and pushing oneself: exertion, striving, and diligent endeavor. The sense of encouragement is a natural extension—urging someone to make that effort.
勉 combines 免 (which here likely contributes the sound) with 力 (strength/effort), suggesting exerting strength or making an effort. The exact historical role of 免 is uncertain, but the phono-semantic structure is broadly accepted.
The top 免 looks like a person straining or escaping, and 力 underneath is strength. Picture someone using all their strength to push through a difficult task—that's exertion and diligence.
For ベン, imagine a diligent student named Ben who always strives to do his best: Ben -> ベン, and his effort is like the 力 inside 勉.
study
diligent; hard-working; industrious
study; pursuit of knowledge
studying like crazy; cramming like a madman
cramming
staying behind after school to do private study
person who studies very hard (at school); grind; swot; drudge
studying for a test
studying for a test
not studying (for a test, etc.); not having studied
idleness; lack of application; lazy study habits
studying two lessons
being arduous; working diligently enduring hardships
diligence
to gain knowledge; to be illuminated
to work hard at one's lessons
insufficient study
while studying; presently studying
cost of a lesson learned (e.g. from failing at something); price of a life lesson
study group; study meeting