# Ball equilibrium between 2 slopes

• carb
In summary, the individual is seeking help in understanding the relationship between the horizontal force, weight, and slopes angle for static equilibrium of a blue ball. They first want to study the problem without considering friction, then with friction between the ball and two planes. They are unsure how to start and suggest possibly beginning with a simpler system without friction. Ultimately, they are looking for the horizontal force needed to achieve equilibrium.
carb
Hello,
Could somebody help me finding the relation between the horizontal force, the weight acting vertically, and the slopes Angle (same for both) that correspond to static equilibrium of the blue ball ?

In a first step, I'd like to study this problem without considering friction at all. And in a second step with friction between the ball and the 2 planes only (but maybe there won't be any difference in the result because of the 2 same planes angles ?)

I think I need to draw a square triangle using the forces but don't know how to start
Any kind of help would be much appreciated!

Maybe I should start with a more simple system ? (no friction at the arrow contact)
I'm seeking for the horizontal force that ensure equilibrium.

Last edited:
In the simpler case:
First find the normal force that needs to be exerted by the slanted plate in order for its vertical component to counter the downward force of the weight. The resultant vector of the weight and the normal force will be the horizontal force on the lower block.

## 1. What is ball equilibrium between 2 slopes?

Ball equilibrium between 2 slopes is a phenomenon that occurs when a ball is placed on two sloped surfaces at different angles and is able to remain stationary without rolling or sliding down either slope. This is due to the balancing forces acting on the ball from the two slopes.

## 2. What factors affect ball equilibrium between 2 slopes?

The factors that affect ball equilibrium between 2 slopes include the angle of the slopes, the weight and mass of the ball, the surface friction of the slopes, and any external forces acting on the ball.

## 3. How does the angle of the slopes affect ball equilibrium?

The angle of the slopes plays a crucial role in ball equilibrium as it determines the balance of forces acting on the ball. When the slopes are at equal angles, the ball will remain stationary at the center. However, as the angles of the slopes differ, the ball will shift towards the steeper slope due to the force of gravity.

## 4. Can the weight and mass of the ball affect ball equilibrium?

Yes, the weight and mass of the ball can affect ball equilibrium as it determines the magnitude of the force of gravity acting on the ball. A heavier ball will require more force to be balanced on the slopes compared to a lighter ball.

## 5. How is ball equilibrium between 2 slopes useful in real-life applications?

Ball equilibrium between 2 slopes has various real-life applications, such as in the design of roller coasters and ski slopes. It also helps in understanding the concept of balance and forces in physics, which has implications in engineering and other fields.

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