Finding Velocity and Pressure of Half-Sphere on Horizontal Plane

It might be easier to use Lagrange's equations as it takes into account the geometry of the problem.In summary, the conversation discusses finding the velocity and maximum pressure of a half-sphere with a given mass and radius, equilibrated on a polished horizontal surface with a wire. The use of Lagrange's equations and Newton's methods are suggested for solving the problem. The half-sphere also behaves like a mathematical pendulum for small angles.
  • #1
Nea
3
0

Homework Statement


The half a sphere with a 'm' mass and 'r' radius is equilibrated on a plan absolutely polished horizontal with the side of the AB wire. So the surface of the half a sphere has with the horizontal plan an alpha angle. Find, after the break of the wire, the velocity of the O center and her maximal value too, also the maximal value of the pressure of the half-sphere over the horizontal. Find that for small angles it behaves like a mathematical pendulum.
Illustration:
http://img135.imageshack.us/img135/9526/fiz1rf6.th.jpg

Homework Equations





The Attempt at a Solution



I think that the lagrange's equations can be employed to solve it.
 
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  • #2
Hello.

I think that using Lagrange's methods won't help you. The best you can do is using Newton... use vectors!

Regards.
 
  • #3
I would use Newton as well but I think it will take some work to draw the components and figure out which contributes to the torque in which way
 

1. What is the formula for finding the velocity of a half-sphere on a horizontal plane?

The formula for finding the velocity of a half-sphere on a horizontal plane is V = √(2gh), where V is the velocity, g is the acceleration due to gravity, and h is the height of the half-sphere above the plane.

2. How do you calculate the pressure exerted by a half-sphere on a horizontal plane?

The pressure exerted by a half-sphere on a horizontal plane can be calculated using the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the half-sphere above the plane.

3. What factors affect the velocity of a half-sphere on a horizontal plane?

The velocity of a half-sphere on a horizontal plane is affected by factors such as the height of the half-sphere, the acceleration due to gravity, and the density of the fluid it is moving through.

4. How does the angle of the plane affect the pressure exerted by a half-sphere?

The angle of the plane can affect the pressure exerted by a half-sphere by changing the height and distance the half-sphere travels, ultimately changing the velocity and pressure calculations.

5. How can the velocity and pressure of a half-sphere on a horizontal plane be used in real-world applications?

The velocity and pressure calculations for a half-sphere on a horizontal plane can be used in various engineering and fluid mechanics applications, such as designing pipelines or calculating the force on a dam. They can also be used to analyze the behavior of objects moving through fluids, such as submarines or airplanes.

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