# Homework Help: Determine the largest angle - wedge

1. Feb 27, 2012

### blackandyello

1. The problem statement, all variables and given/known data
A small wedge is placed beneath corner B of the 4000-kg block of marble.
Determine the largest angle θ for which the wedge is self-locking; that is, the
wedge will not slide out from under the block. Neglect the mass of the wedge and
the small angle between surface AB and the horizontal.

http://screensnapr.com/e/527Zk6.jpg [Broken]

2. Relevant equations

using the FBD of the whole composite body.

summation of forces on x = 0
0.2Na - 0.2Nc = 0

summation of forces on y = 0
-39240 + Na + Nc = 0

solving, it yields = Na = 19620 Nc = 19620

3. The attempt at a solution

now, we take the fbd of just the wedge

summation of forces along x = 0
Nb cos(90-θ) -fb cos(θ) - fc = 0

summation of forces along y = 0
-Nb sin(90-θ) - fb sin(θ) + Nc = 0

dividing those 2 eqns yields:

-tan(90-θ) + tan(θ) - (Nc/fc)
then since we have Nc and Fc (using f = uN) where u = 0.2

and θ yields arounds 70 degrees which is incorrect (the book says 18.15 degrees)

thanks

Last edited by a moderator: May 5, 2017