A block of mass 11 kg is at rest on a rough plane inclined at 30° to the horizontal. A force acts on the block in a direction up the plane parallel to a line of greatest slope. When the magnitude of the force is 2X N the block is on the point of sliding down the plane, and when the magnitude of the force is 9X N the block is on the point of sliding up the plane. Find the value of X.

Question

My work so far isn't much, just one equation: 9X - F = 110sin30

I know that I have to get another equation and cancel them out the same way you'd do  simultaneous equations, but I'm not so sure how to get the second one.

Thanks for the help!

Scott · Accepted Answer

forces on the block are
... friction (F) ... opposing motion up or down
... gravity (G) ... downward along plane
... X force ... upward along plane

gravitational force perpendicular to the plane is part of the frictional force

G = F + 2X

G + F = 9X

you already have G as 110 sin(30º)

eliminate F , and you've got it