Mechanical Work is defined as W=FD. Where F is a constant force. The force is parallel to the displacement(providing theta = 0) and in the same direction.

Why do we multiply Force TIMES distance? It's the multiplication that confuses me

Drakkith
Staff Emeritus
If you push a cart weighing 10 kg with a constant force, it takes double the work to move it twice the distance. Hence force x distance.

russ_watters
Mentor
"Why" is a difficult question here. Ultimately, some guy saw FD as a useful thing to know and gave it the name "work". Beyond that, I'm really not sure what you are looking for.

Work is really about the transfer of energy (not heat, though) from one thing to another. The amount of energy imparted to an object is directly related to 1) the force acting on the object, and 2) the distance the object travels. Since the amount of energy imparted to an object increases when both force and distance increase, they get multiplied together.

Since the amount of energy imparted to an object increases when both force and distance increase, they get multiplied together.

russ_watters
Mentor
Well for starters, you can't add quantities together that have different units....

sophiecentaur
Gold Member
2020 Award
F·dx=ma·dx=mdv/dt·dx=mdv·dx/dt=mvdv⇒∫F·dx=½mv²+constant. Similarly for the impulse,