Homework Help: Ball in a wedge Equillibrium

Dtails · Dec 4, 2008

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?

mathmate · Dec 4, 2008

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.

Dtails · Dec 4, 2008

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!

mathmate · Dec 4, 2008

Sin([tex]\theta[/tex]) = opposite / hypotenuse
Cos([tex]\theta[/tex]) = adjacent / hypotenuse

Dtails · Dec 4, 2008

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.

mathmate · Dec 4, 2008

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?

Dtails · Dec 4, 2008

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