# Thread: Resolving normal components with 2 slopes

1. ## 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.

2. Hi

Do not forget the weight of the ball
The equilibrium is given by $\vec{P} + \vec{Q} + m\vec{g} = \vec{0}$
You can do the projection of this vectorial equality on any axis, for instance on each plane

3. I don't know how to resolve these forces in any particular direction due to the different angles.

4. Look at the sketch below

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' ?

5. I have the angle between P and xx' as 30 degrees
Q xx' 90 degrees
and mg and xx' as 70 degrees

Correct?

6. Yes correct
Now you are able to do the projection of the vectorial relation on xx'