# Resolving normal components with 2 slopes

• May 15th 2011, 06:52 AM
elieh
Resolving normal components with 2 slopes
The diagram (attached) shows a small ball of mass 2 kg, resting in the horizontal groove between two smooth planes inclined 20 degrees and 40 degrees to the horizontal. Find the magnitudes of the contact forces P and Q.

I know I have to resolve the forces in one direction but I'm stuck cause I don't have any angles.

Since it's in equilibrium the sum of all the forces in each direction is equal.
Help appreciated.
• May 15th 2011, 07:09 AM
running-gag
Hi

Do not forget the weight of the ball
The equilibrium is given by $\displaystyle \vec{P} + \vec{Q} + m\vec{g} = \vec{0}$
You can do the projection of this vectorial equality on any axis, for instance on each plane
• May 15th 2011, 07:25 AM
elieh
I don't know how to resolve these forces in any particular direction due to the different angles.
• May 15th 2011, 07:44 AM
running-gag
Look at the sketch below

http://img861.imageshack.us/img861/7455/exercise.jpg

Axis xx' is parallel to the plane on the left
We choose to project the vectorial relation on xx' (oriented upwards)
What is the angle between P and xx', between Q and xx', between mg and xx' ?
• May 15th 2011, 07:59 AM
elieh
I have the angle between P and xx' as 30 degrees
Q xx' 90 degrees
and mg and xx' as 70 degrees

Correct?
• May 15th 2011, 08:09 AM
running-gag
Yes correct
Now you are able to do the projection of the vectorial relation on xx'