Solid hemisphere resting on an inclined plane

In summary, the problem involves a solid uniform hemisphere resting in equilibrium with a rough inclined plane elevated at an angle α, where sin(α) = 3/16. The goal is to find the angle between the symmetry axis of the hemisphere and the vertical. The solution involves using the sine rule and drawing the hemisphere and incline in a specific orientation.
  • #1
Jamessamuel
45
0

Homework Statement



A solid uniform hemisphere rests in equilibrium with its curved surface in contact with a rough inclined plane which is elavated by an angle α where sin(α) = 3/16. Find the angle between the symmetry axis of the hemisphere and the vertical.[/B]

Homework Equations


Sine rule

The Attempt at a Solution


I drew the hemisphere as though slightly tilted - so that the line of action of the weight passed through the contact point of the hemisphere with the plane. However the answer shows the hemisphere so that the flat surface is vertical and not only do I fail to understand how this arrangement would keep it on equilibrium but also how I was supposed to know to draw it in this orientation.
 
Physics news on Phys.org
  • #2
image.jpg
 
  • #3
You are right. The flat surface would not be vertical. Use the triangle shown on the right as a guide to drawing the hemisphere and incline.
 

1. What is the force acting on the solid hemisphere resting on an inclined plane?

The force acting on the solid hemisphere is the weight of the object, which is equal to its mass multiplied by the acceleration due to gravity. This force is directed downwards and can be resolved into two components - a normal force perpendicular to the plane and a frictional force parallel to the plane.

2. How is the angle of inclination related to the normal force on the solid hemisphere?

The normal force on the solid hemisphere is equal to the component of the weight acting perpendicular to the plane. As the angle of inclination increases, the component of the weight acting perpendicular to the plane decreases, resulting in a decrease in the normal force.

3. What is the maximum angle of inclination at which the solid hemisphere will remain at rest?

The maximum angle of inclination at which the solid hemisphere will remain at rest is when the normal force is equal to the weight of the object. This occurs when the angle of inclination is equal to the arctangent of the coefficient of friction between the object and the plane.

4. How does the mass of the solid hemisphere affect its stability on the inclined plane?

The stability of the solid hemisphere on the inclined plane is affected by both its mass and the angle of inclination. As the mass increases, the normal force also increases, making it more stable on the plane. However, if the angle of inclination is too great, the weight of the object may overcome the normal force and cause it to slide down the plane.

5. Can the solid hemisphere roll down the inclined plane?

Yes, the solid hemisphere can roll down the inclined plane if the angle of inclination is great enough and the frictional force is not strong enough to prevent it from sliding. The object will roll down the plane due to the torque created by the weight acting on the object at a distance from its center of mass.

Similar threads

To find the weight of a hemisphere
    • Introductory Physics Homework Help
Replies
13
Views
1K
Two solid hemispheres, one resting on top of the other
    • Introductory Physics Homework Help
Replies
12
Views
1K
Stable Equilibrium of Stacked Hemispheres
    • Introductory Physics Homework Help
Replies
1
Views
2K
Statics on an inclined plane
    • Introductory Physics Homework Help
Replies
23
Views
3K
Normal force on slipping hemisphere
    • Introductory Physics Homework Help
Replies
18
Views
2K
Block at rest on an inclined surface
    • Introductory Physics Homework Help
2
Replies
36
Views
4K
Equilibrium of a stiff plate on inclined planes
    • Introductory Physics Homework Help
Replies
31
Views
3K
Question Concerning The Coefficient of Friction: Block on a Rough Inclined Plane
    • Introductory Physics Homework Help
Replies
5
Views
1K
Spring on an inclined plane
    • Introductory Physics Homework Help
Replies
5
Views
1K
Block on an inclined plane that is accelerating sideways
    • Introductory Physics Homework Help
Replies
27
Views
3K

Hot Threads

Recent Insights

Back
Top