See if you can solve this, first right answer gets Best Answer?

Question

While studing for a mechanics test, I created a problem that no one I knew including my professor could solve. I eventually solved it, and would like to see who else can.

You have a massless inclined plane whose angle is Theta. There is no friction or gravity anywhere in the problem. There is a block of mass M on the incline. You apply a force to the vertical part of the incline of F. The incline is attached to a rail so that it can only move left and right, so no up or down movement, and no rotation.

Remember no friction of gravity, massless inclined, M mass block, force F applied parallel to the base of the block to push it along the frictional rail.

What is the acceleration of the inclined Plane at any angle where theta is between 0 and 90 not inclusive. (at 90 they act as one piece, so its easy, and at 0 a force cant be applied at all!)

Good Luck!

im in my second year of college, why would you need to know?

Answer 1

OK I think I understand what your asking. The incline is like a wedge, so the horizontal force F is acting on the vertical part of the wedge. Fine.

Forces on the block:
R = normal reaction between the incline and the block
ab = acceleration of block
ai = acceleration of incline
R = M*ab
Relative to the incline the block slides up (without friction), so we can construct a right angle triangle to get a relation between ab and ai, which is
ab / ai = sinθ
ab = ai * sinθ

Forces on incline:
Vertically the normal reaction at the ground cancels off the vertical component of R.
Horizontally, F - Rsinθ = 0*ai
Thus F = Rsinθ
= M*ab * sinθ
= M*(ai * sinθ) * sinθ
= M* ai * sin^2 θ

So ai = F / (M * sin^2 θ)

Answer 2

Here's my best guess:
Since you said there's no gravity or friction anywhere in the problem...
a = F / (m*sin theta) m/s/s
or if that's wrong, my only other second guess is 0 m/s/s.

Answer 3

holy crap what grade r u in?