A block of mass m sits at rest on a rough inclined ramp that makes an angle θ with the horizontal. What must be true about force of static friction f on the block?

Answer: So the static friction force must be equal to g*m*cos (θ)

Explanation: The force downwards of the block will be equal to the component with respect of where it can move.

So the force downwards will be:

F = Weight*cos (θ)

And we know that the weight is w = - m*g where g is the gravitational acceleration.

F = - g*m*cos (θ)

And we know that the block is at rest, so the net forces on it are equal to zero, this means that the gravitational force must be canceledby other one, and this can be the static friction force.

So the static friction force must be equal to g*m*cos (θ)