Determine the force P required to start the wedge. the angle of friction for all surfaces in contact is

Question

15degrees...

here's the figure: http://i20.photobucket.com/albums/b243/bhabyabie/mechanics.jpg

Answer 1

There are at least two ways of doing it.

One easy way to recognize that if there is no friction, a simple machine like a wedge conserves energy.

Energy = force x distance

That means that if the wedge moves down X and the block moves to the right a distance Y, then:

X P = 500 Y or P = 500(Y/X)

Now this is a simple geometry problem, and Y/X = tangent of the wedge angle. You know the wedge angle, so you can compute its tangent and then P.

The long way 'round basically just proves the result above:

let N be the normal force on the sloped side against which the wedge acts.

The you can decompose N into a vertical component and a horizontal component, using the angle.

Then you have the equations:

Nh = 500

Nv = P

The 2000 lb vertical force on the block doesn't enter into anything unless there is friction. If there is friction on the horizontal surface but not on the vertical, then the 500 lb horizontal force that P has to overcome become 500 + Fs, where Fs is the force of static friction:

Fs = 2,000 x Ks where Ks is the coefficient of static friction.

If there is also friction on the inclined surface, then the equations get more complicated yet, as you can't assume an ideal machine and the force N generates a frictional force that also has vertical and horizontal components that you have to take into account.