I'm getting a bit confused when finding components of vectors and forces.
In problems for vectors, I've always known that if you want to get the components of a vector, you would use the following:
Recently we've started working with Forces in homework problems.
This diagram is from one of my homework problems, which they want me to draw the free body diagram:
Here is the free body diagram given by the homework solution:
What I don't understand is why would I be using $m_{2}gsin(\theta)$ instead of $m_{2}gcos(\theta)$ when finding the X-component of the gravitational force of $m_{2}$.
Force is a vector, so why wouldn't you use $m_{2}gcos(\theta)$? Are the rules different when dealing with forces?
Best Answer
It depends how you define the angle. In this diagram you define the angle with respect to the horizontal and take the x-axis along the slope. So the x-component of of gravitational force comes out to be $m_2gsin\theta$. If you define the angle $\theta$ with respect to the vertical, then you would see $m_2gcos\theta$ as the x-component of the gravitational force. So it all depends on how you define the angle of slope.