An object rolling along a hemispherical bowl

  • Thread starter Momentum09
  • Start date
  • Tags
    Rolling
In summary, a uniform solid sphere of mass 1.5kg and radius 0.473m is released from rest at an angle of 66.9 degrees from the vertical on the inside surface of a hemispherical bowl of radius 2.77m. The sphere rolls without slipping and we are asked to find the potential energy lost, translational velocity, and angular velocity when it reaches the bottom of the bowl. Using the equations for potential energy and kinetic energy, we can find the potential energy lost and set it equal to the total final energy, which is the sum of the translational and rotational kinetic energies. By setting these equal, we can find a relation between the angular velocity and the linear velocity, as the sphere
  • #1
Momentum09
71
0

Homework Statement



A uniform solid sphere (moment of inertia = 2/5 mr^2) of mass 1.5kg and radius r = 0.473m, is placed on the inside surface of a hemispherical bowl of radius R = 2.77m. The sphere is released from rest at an angle of 66.9 degrees from the vertical and rolls without slipping.
a) How much potential energy has the sphere lost when it reaches the bottom of the bowl?
b) What is the translational velocity of the sphere when it reaches the bottom of the bowl?
c) What is the angular velocity of the sphere when it reaches the bottom of the bowl?

Homework Equations



KE = 1/2 Iw^2. PE = mgh.

The Attempt at a Solution



For part a, do I just do (1.5kg)(9.8)(2.77sin66.9)?
After I find PE, I will just equate it with 1/2 mv^2 to find the translational velocity and 1/2 Iw^2 to find the angular velocity?

Any help is appreciated. Thank you!
 
Physics news on Phys.org
  • #2
Momentum09 said:
For part a, do I just do (1.5kg)(9.8)(2.77sin66.9)?
After I find PE, I will just equate it with 1/2 mv^2 to find the translational velocity and 1/2 Iw^2 to find the angular velocity?

Any help is appreciated. Thank you!
part a looks fine. part b is not fine. the total energy initially is PE + KE_trans + KE_rot. this must equal the total final energy PE_f + KE_trans_f+KE_rot_f. Part a is the value of PE and PE_f=0.

thus set PE = KE_trans_f + KE_rot_f

not equal to each individually.
 
  • #3
And find a relation between the angular velocity and the linear velocity, since it 'rolls without slipping'.
 
  • #4
I got it. Thank you so much!
 

Related to An object rolling along a hemispherical bowl

1. What is the physics behind an object rolling along a hemispherical bowl?

When an object rolls along a hemispherical bowl, it follows the principles of circular motion and conservation of energy. It experiences a centripetal force towards the center of the bowl, which keeps it moving in a circular path. The object also has kinetic and potential energy, which are constantly being converted as it rolls.

2. What factors affect the speed of an object rolling along a hemispherical bowl?

The speed of the object is affected by the radius of the bowl, the mass and shape of the object, and the angle at which it is released. A larger radius will result in a higher speed, while a smaller mass and a steeper angle will also increase the speed.

3. How does the shape of the bowl affect the motion of the rolling object?

The shape of the bowl plays a crucial role in the motion of the rolling object. A hemispherical bowl provides a constant radius for the object to follow, resulting in a consistent speed. If the bowl is not perfectly hemispherical, the radius may change, causing the object's speed to vary.

4. What is the difference between the motion of an object rolling along a hemispherical bowl and a flat surface?

The main difference between the two is the presence of a centripetal force in the hemispherical bowl. This force is not present on a flat surface, which means the object can continue rolling at a constant speed without any external force acting upon it. Additionally, the potential energy of the object is constant on a flat surface, while it changes in a hemispherical bowl due to the varying radius.

5. Can an object roll indefinitely along a hemispherical bowl?

No, an object cannot roll indefinitely along a hemispherical bowl due to friction. As the object rolls, it experiences frictional forces that slow it down, eventually causing it to stop. Additionally, the potential energy of the object decreases as it rolls, also contributing to its eventual stop. This is why a perpetual motion machine is not possible.

Similar threads

Why Is Deriving the Motion Formula for Hoops More Complex?
    • Introductory Physics Homework Help
Replies
4
Views
242
Wooden sphere rolling on a double metal track
    • Introductory Physics Homework Help
3
Replies
97
Views
3K
Acceleration of system related to rolling motion and pulley
    • Introductory Physics Homework Help
2
Replies
35
Views
2K
Friction Required for Billiard Ball to Roll without Slipping
    • Introductory Physics Homework Help
2
Replies
60
Views
442
Kinetic Energy of a Cylinder Rolling Without Slipping
    • Introductory Physics Homework Help
Replies
21
Views
2K
Moment of inertia problem involving a cylinder rolling down an incline
    • Introductory Physics Homework Help
Replies
11
Views
1K
Conservation of energy problem: Ball rolling down inclined plane and then through a loop-the-loop
    • Introductory Physics Homework Help
Replies
10
Views
511
Mechanics: A bowling ball is thrown and rolls with slipping
    • Introductory Physics Homework Help
Replies
8
Views
3K
Question regarding Rolling with and without Slipping and Sliding
    • Introductory Physics Homework Help
Replies
4
Views
1K
How Does a Marble's Speed Change as It Rolls Down a Hemispherical Bowl?
    • Introductory Physics Homework Help
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top