Movement of object when F more than Fs

[werson tan]

Homework Statement

Although F is more than Fs , the object still wouldn't slide down due to 100N is still greater than 80 N ...Why the book gave that the obejct will start to slide down ?

Homework Equations

The Attempt at a Solution

 

[Simon Bridge]

The ramp is at angle A so that it forms the hypotenuse of a 3-4-5 triangle, with the 4-side horizontal.
so tanA=3/4, sinA=3/5, and cosA=4/5

There is friction too, coefficients given as 0.25 and 0.2 for static and kinetic respectively.

We need to know if the block is in equilibrium - i.e. do the forces add to zero.

The normal force automatically cancells the component of weight along it's axis, leaving the components along the ramp to sort out.
Is the applied force of 100N big enough to balance the block?
100N < (3/5)300N = 180N so no - any friction must act up the ramp.

The amount of force the friction must balance is 180N-100N = 80N acting down the ramp. This is what happened to that 100N you were wondering about.
Static friction supplies a maximum of (0.25)(4/5)300N = 60N ... so static friction is no enough to overcome the remaining force.
Therefore, the block slides down the ramp.