A5.0-kg crate is on an incline that makes an angle 30° with the horizontal. if the coefficient of static friction is 0.5, what is the maximum force that can be applied parallel to the plane without moving the crate?

Explanation:

When maximum force is applied on the crate along the plane so that it will not move then in that case friction force and component of the weight of the crate is along the plane opposite to the applied force

So here we will have

now we know that

also we know that

so we will have

now we will have

so we will have

since you're a real machine, your ama is always less than your ima, because you can never totally eliminate friction.