- #1

- 679

- 30

Let ##\vec{a}## be the gravitational acceleration along the curve.

Then ##|\vec{a}|=a=-g\sin\theta## and

##\vec{a}=a_x\,\vec{i}+a_y\,\vec{j}=-g\sin\theta\cos\theta\,\vec{i}-g\sin^2\theta\,\vec{j}##

My question is why does the solution below ignore the direction of ##\vec{a}## and calculate ##F## as ##F=\int a\,dm## instead of calculating ##\vec{F}## as ##\vec{F}=\int a_x\,dm\,\vec{i}+\int a_y\,dm\,\vec{j}##?

Solution: