How Do Forces Act on Spheres in a Rectangular Container at a 45 Degree Angle?

In summary, the problem involves two identical, uniform, and frictionless spheres of mass m in a rigid rectangular container. The spheres are positioned so that a line connecting their centers is at a 45 degree angle to the horizontal. The forces on the spheres from the bottom, left side, and right side of the container are all equal to mg, while the force between the two spheres is equal to mg multiplied by the square root of 2. This is because the forces between the spheres are directed along the center-center line, while the forces from the walls and floor of the container are normal.
  • #1
PremedBeauty
25
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Two identical, uniform, and frictionless spheres, each of mass m, rest in a rigid rectangular container. A line conecting their centers is at 45 degrees to the horizontal. Find the magnitudes of the forces on the spheres from (a) the bottom of the container, (b) the left side of the container, (c) the right side of the container and (d) each another. (Hint: The force of one sphere on the other is directed along the center-center line)
I'm sorry, the image is off alittle (I'm a lefty and this mouse is on the right side) but the two balls are touching the walls, and the w's are supposed to be in the center of the spheres. :uhh:
 

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  • #2
You stated the problem, but where's your attempted solution? Show what you've done and point out where you got stuck.

Hint: Since the spheres are frictionless, what must be true about the contact forces acting on them?
 
  • #3
solution

solution:
The contact force exerted by the lower sphere on the upper is along that is 45o and the forces exerted by the walla and floors are normal.

Equilibrium force on the top sphere leads to

Fwall = F cos 45 and F sin 45 = m g

According to Newtons third law the equilibrium of forces on the bottom sphere leads to

F'wall = F cos 45 and F'floor = F sin 45 +mg

a)magnitudes of the forces on the spheres from the bottom of the container

F'floor = mg +mg = 2mg
b)magnitudes of the forces on the spheres from the left side of the container

F'wall = mg
c))magnitudes of the forces on the spheres from the right side of the container

F'wall = mg
d) magnitudes of the forces on the spheres from each other

F = mg / sin 45 = mg * √2

Is that correct?
 
  • #4
Looks good to me!
 
  • #5
Thank you. I was wondering if it's correct when I did it.
 
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1. What is equilibrium in physics?

Equilibrium in physics refers to a state in which the forces acting on an object are balanced, resulting in no net force and no change in motion. In other words, the object is either at rest or moving at a constant velocity.

2. How is equilibrium related to elasticity?

Equilibrium and elasticity are closely related concepts. In order for an object to be in equilibrium, the forces acting on the object must also be in a state of balance. Elasticity is the property of a material that allows it to return to its original shape after being deformed by an external force. This means that when an object is in equilibrium, it is also in a state of elastic balance.

3. What is the difference between static and dynamic equilibrium?

Static equilibrium refers to a state in which an object is at rest and the forces acting on it are balanced. On the other hand, dynamic equilibrium refers to a state in which an object is moving at a constant velocity and the forces acting on it are balanced. Both types of equilibrium are important in understanding the behavior of objects in different situations.

4. How is the concept of equilibrium used in engineering?

Equilibrium is a fundamental concept in engineering, as it allows engineers to analyze the forces acting on structures and design them to withstand these forces. By understanding equilibrium, engineers can ensure that structures are stable and able to support the expected loads without failing.

5. What factors affect the elasticity of a material?

The elasticity of a material depends on several factors, including the type of material, its molecular structure, and the conditions under which it is being deformed. Temperature, pressure, and the rate of deformation can all affect the elasticity of a material, as well as any previous deformation or damage to the material.

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