Finding Angle Which Cube Falls Off Sphere

In summary, the conversation discusses the movement of a cube on top of a hemisphere. The coefficient of kinetic friction is equal to the coefficient of static friction for the two surfaces. The cube is given a small nudge and begins to slide down the side of the hemisphere, eventually losing contact. The conversation then explores different scenarios with different values for the initial speed and coefficient of friction, and suggests using summation of forces for circular motion and conservation of energy to solve for the angle at which the cube falls off the sphere. The conversation also references a helpful online discussion for further understanding.
  • #1
apierron
11
0
A cube of polished steel sits on top of a highly polished and waxed hemisphere of polycarbonate (radius 92 cm). For these two surfaces interacting, the coefficient of kinetic friction is the same as the coefficient of static friction. The cube is given a very small 'nudge' perpendicular to the center of the cube and tangent to the top of the hemisphere. The cube starts to move with an initial speed. As the cube slides down the side of the sphere, it eventually loses contact with the surface of the sphere.



a.) Assume μ is zero and that the initial speed is also zero to solve for the angle (relative to the vertical) at which the cube falls off of the sphere.

b.) How does your answer to a change if the initial speed is not zero, but is 50cm/s? Discuss your results qualitatively (what changes and why) and describe them quantitatively (solve for the angle relative to the vertical at which the cube falls off).

c.) Assume that μ is 0.1 and that the initial speed is zero to solve for the angle.

d.) How does your answer to c change if the initial speed is not zero, but is 50cm/s? Discuss you results qualitatively (what changes and why) and describe them quantitatively (solve for the angle relative to the vertical at which the cube falls off).



I tried drawing a free body diagram and maybe looking at the forces that act on the cube but then I just got confused. Am I supposed to relate uniform circular motion into any of this? I attached a picture of the problem.
 

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  • #2
I forgot, he also gave us the length of one side of the cube as 3cm
 
  • #3
Okay so I took another look at this problem and I'm pretty sure I went about it all wrong. My new approach would be to take the ∫F ds, where F would be the sum of my forces and ds would be the change in arc length. I started working this out and I just don't know what to set my limits as and what I would set this equal to, so that I could solve for θ. I thought maybe I could set it equal to zero since the only work done on the object is gravity but I'm not sure. Can anyone tell me if I'm headed in the right directions and give any hints to what I'm having trouble with?
 
  • #4
Hi Amber

I suggest using summation of forces for circular motion as well as conservation of energy.
Since energy conservation and summation of radial forces hold at any point for the cube-sphere system, that should get you there.
 
  • #5
The Anonymous said:
Hi Amber

I suggest using summation of forces for circular motion as well as conservation of energy.
Since energy conservation and summation of radial forces hold at any point for the cube-sphere system, that should get you there.

Okay thanks! I think that will be way easier than what I was trying to do.
 
  • #6
Once you include the effects of friction, then you'll need to evaluate the path integral for the friction force from theta=0 to theta=theta critical, but that'll end up being a lot like the example I did in class last week.

cheers
 

1. What is the "Finding Angle Which Cube Falls Off Sphere" experiment?

The "Finding Angle Which Cube Falls Off Sphere" experiment is a physics experiment that involves placing a cube on top of a sphere and gradually tilting the sphere until the cube falls off. The angle at which the cube falls off is then measured and analyzed.

2. Why is the "Finding Angle Which Cube Falls Off Sphere" experiment important?

This experiment helps to demonstrate the concept of center of mass and how it affects the stability of an object. It also helps to understand the relationship between the angle of tilt and the force of gravity acting on an object.

3. What materials are needed for the "Finding Angle Which Cube Falls Off Sphere" experiment?

The materials needed for this experiment include a sphere, a cube, a protractor, a ruler, and a flat surface to perform the experiment on.

4. How is the angle at which the cube falls off measured?

The angle is measured using a protractor by aligning the flat edge of the protractor with the surface of the sphere and the base of the protractor with the ground. The angle at the point where the cube falls off is then read from the protractor.

5. What are some possible sources of error in the "Finding Angle Which Cube Falls Off Sphere" experiment?

Some possible sources of error include uneven surfaces, imprecise measurements, and external factors such as air resistance. It is important to repeat the experiment multiple times and take an average of the results to minimize these errors.

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