Getting confused on inclines and translational motion

[phattestlewt]

Given an incline plane with angle theta, a box is sliding down, include friction.

I'm getting confused on how to calculate the acceleration of the box sliding down.

0=theta
if F = ma = mgsin0 - Friction

^is that it?

And is it possible to calculate the acceleration of the box in the y-direction, if so what is it?

---

Members don't see this ad.

 

[Timorito]

well you only have horizontal acceleration so you only work in the y plane. so make your acceleration in direction with your movement. f equals mgsin theta minus friction. so a is gsin theta

 

[Blueprint MCAT Tutor]

I'm not sure if I understand exactly what you're asking.

The acceleration down the plane is:

a = g sin θ (my mnemonic here is "s for sine, s for sliding down the slide, so the a and F vectors that point sliding down the slide have to be multiplied by sine")

If you're asking how to break up that vector pointing down the plane into vectors in the x and y direction, I think it would look like this:

http://i.imgur.com/mvJAEAY.png

That's really sloppy, but it was just me working things out super quick on scratch paper. The idea here is that the hypotenuse of the triangle is "g sin θ" and then you can just use sin and cos to find the other two sides of the triangle.

I did an example with a θ of 30 to show that you end up with a right triangle with a base of 4.3 a height of 2.5 and a hypotenuse of 5. That all seemed reasonable to me.

Oh and if there's friction I guess it would be:

a = g sin θ - μg cos θ