Ball in a wedge Equillibrium

1. Dec 4, 2008

Dtails

1. The problem statement, all variables and given/known dataA solid sphere of radius 1 m and mass 5 kg
is placed in a wedge with θ = 29 ◦
The inner surfaces of the wedge
are frictionless.
The acceleration of gravity is 9.8 m/s2 .
Determine the force exerted by the wedge
on the sphere at point B. Answer in units
Figure, ASCII style!
| /
|O/ <-b
v

point a is on the flat side towards the ball.

Edit: I realize that the ascii diagram may suck, but.
2. Relevant equations
Fnet=0

3. The attempt at a solution

Alright, so I tried this.
Fx=a+bcos(119)
Fy=bsin(119)-5*9.8.

This shouldn't be as annoying as it is. I mean, by my method, B is easily given, but the answer i get is wrong. Which means I'm not seeing something. Ideas?

2. Dec 4, 2008

mathmate

If you draw the triangle of forces acting on the ball, there the the horizontal reaction A (towards the right), joined to the reaction B upwards and to the left, and the vertical force representing the weight of 5 kg. (5*9.8)

|<\
|**\B
|***\
v---->
...A

The * are just fillers to make a nicer triangle, ignore them.
The angle between A and B is 29 degrees.
So if you try to solve this right triangle, you will get the values of A and B.

3. Dec 4, 2008

Dtails

Just tried the triangle, just gave me the same answer as the vector resolution. :/

5*9.8/sin61 = 56.024349 Which apparently is not the answer.

This is why it's annoying! The intuitive answers are always wrong!

4. Dec 4, 2008

mathmate

Sin($$\theta$$) = opposite / hypotenuse
Cos($$\theta$$) = adjacent / hypotenuse

5. Dec 4, 2008

Dtails

Well I hope I know that xP But yeah. From your triangle, the 29 degree shoots up to the top of the triangle, and the 61 becomes the most useful for a sin substitution. hence 5*9.8/b=sin61, so 5*9.8/sin61=b. :/ Not sure if i'm screwing up somewhere.

6. Dec 4, 2008

mathmate

The (lousy) triangle I drew is a triangle of forces which has to close for equilibrium.
Force A is the normal (90degrees) to the vertical side, so it is horizontal.
Force B is the normal to the slanting side, so it makes 29 degrees with the horizontal.
Well, the vertical component is mg=5*9.8, which I am sure you know.
Want to give it another try, if you are solving for B?

7. Dec 4, 2008

Dtails

Hah, I fail epiclly at Trig. xD Sin29 worked like a charm, on the last try, too. Thanks, man.