Solving for Equilibrium Forces on a 5kg Ball

[Bhupendra]

Homework Statement

a spherical ball of mass = 5kg rests between two planes which make angles of 30 degrees and 45 degrees respectively with the horizontal . The system is in equilibrium . find the normal forces exerted on the ball by each of the planes . The planes are smooth .

Homework Equations

Let Normal force of 30 degree plane be R1 and of 45 degree be R2

The Attempt at a Solution

since , the system is in equilibrium i have balanced all the normal forces and equated but the expression is not right .
The correct answer is R1 - mgsin150 degrees / sin165 degrees
R2 = mgsin45 degree / sin 165 degrees

 

[Orodruin]

Could you show us your attempt at balancing the forces?

Generally speaking, which forces are going to act on the ball and in which directions do they act?

 

[Bhupendra]

i have made the component of the normal forces acting on the ball from both the planes something like this.

 

[Orodruin]

So your first problem would seem to be that your diagram does not look like that in the problem. Instead of taking the 45 degrees from the same direction as the 30 degree angle, you have taken it from a direction 180 degrees away from it. I suggest you look at the picture attached to your first post and make a new attempt.

 

[Bhupendra]

sir i have tried hard and did not get the result that's why i am here to clear my doubt please help me by explaining me the concept .

 

[Orodruin]

I think you already have the concept but have misunderstood the problem. However, I cannot tell for sure unless you correct the misunderstanding in the problem formulation. If you read my previous message, your sketch seems to assume that the angle between the planes is 105 degrees. According to the illustration you attached in your first post, the angle between the planes should be 15 degrees.

 

[Bhupendra]

yeah i have tried with that too and got this

 

[Orodruin]

I would suggest you to make a more accurate drawing where both planes lean to the right. As it is now, I believe you are confusing yourself with the directions of the forces based on your drawing. Remember that the forces need to be normal to the planes.