Equations of movement of partical that slides inside a container

In summary, the speakers are discussing a problem involving finding the equations of movement for a particle in a spherical container. They mention using F=ma and different methods, such as the pendulum, to solve the problem. The possibility of using spherical coordinates is also brought up.
  • #1
alejandro7
13
0
Hello

I'm trying to solve the following problem:

"Find the equations of movement of a particle of mass m that slides on the inner surface of a spherical container given by the equation x^2 +y^2 + z^2 = 1, z≤0"

I know I have to use F=ma and I've tried derivating the equation but I don't get anywhere.

Thanks.
 
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  • #2
The pendulum is a similar problem.
It is a particle moving in a plane and constrained to stay on a circle.
Have a look at how this is usually treated, this might inspire you.
You will see the decomposition of the forces into a component tangential to the trajectory (T) and one perpendicular (N) to it.

You should inform us also on the context of this exercise.
If this is supposed to be an application of the Lagrange method, then i is another story.
 
  • #3
No, there is not optimization involved in the problem. I'm familiar with the pendulum but the relation between vectors (with vector calculus notation) and forces is confusing me.
 
  • #4
The question about the Lagrange method was really about the Lagrange equation of motion. But from your answer it seems you are not aware of that.

This problem is best solved in spherical coordinates. Are you familiar with them?
 
  • #5
Oh, my bad. Yes, but is it necessary? What is the best path to follow?
 
  • #6
alejandro7 said:
Oh, my bad. Yeso, but is it necessary?

What "it"?

What is the best path to follow?

In my opinion, use spherical coordinates.
 
  • #7
It = using spherical coordinates. I will try that.
 

FAQ: Equations of movement of partical that slides inside a container

1. What is an equation of movement for a particle sliding inside a container?

An equation of movement for a particle sliding inside a container is a mathematical representation that describes the position, velocity, and acceleration of the particle at any given time. It takes into account the forces acting on the particle and the properties of the container.

2. How do you calculate the position of a sliding particle at a given time?

The position of a sliding particle at a given time can be calculated using the equation: x(t) = x0 + v0t + (1/2)at^2, where x0 is the initial position, v0 is the initial velocity, a is the acceleration, and t is the time.

3. What factors affect the velocity of a sliding particle inside a container?

The velocity of a sliding particle inside a container is affected by various factors such as the initial velocity, the force of gravity, the surface of the container, and any external forces acting on the particle.

4. How does the shape of the container impact the equation of movement for a sliding particle?

The shape of the container can impact the equation of movement for a sliding particle by changing the magnitude and direction of the forces acting on the particle. For example, a particle sliding in a curved container will experience centripetal acceleration, which will affect its velocity and position.

5. Can the equation of movement for a sliding particle be used to predict future positions?

Yes, the equation of movement for a sliding particle can be used to predict future positions by plugging in the initial conditions and solving for the desired time. However, this prediction may not be entirely accurate as it does not take into account external factors such as air resistance, friction, or changes in the container's surface.

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