(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello all, kinda angry at myself for posting this but my brain has hit a brick wall.

This is an easy problem too... anyway.

A frictioness ramp of massMand inclineθsits on a frictionless surface. A block of massmsits on the ramp. What horizontal forceFmust be applied to the ramp to ensure the block does not move?

2. Relevant equations

F = ma

Newton's Third Law

3. The attempt at a solution

I know the answer is (m+M)*g*tan(θ). But I'm having trouble making myself believe it.

I started with a force diagram of the block, the only 2 forces acting on it are gravity directly downward and the normal force (N) at an angle of θ above the horizontal.

So the net force on the block is F[itex]_{block}[/itex] = N sin(θ) i + (mg-(N cos(θ)) j = ma

Then I looked at the ramp+block system and determined

F[itex]_{system}[/itex] = (M+m)a[itex]_{system}[/itex]

Here for some reason the gears stop turning. I went on to say that the y components on the block sum to zero, so the Normal force is [itex]\frac{mg}{cosθ}[/itex].

From here I substitued in for N in the x direction and then equated "a" in both equations but I know that's wrong. Got me the right answer, but its the wrong way of doing it. Any help would be appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Applied Force to a Sliding Frictionless Ramp

**Physics Forums | Science Articles, Homework Help, Discussion**