Acceleration ball rolling on a parabola

In summary, the problem is that the equation given is variating and the user needs to find a solution for its general form. They are also trying to find the fastest way for a ball to move from Point A to B. The user has found a solution for the straight line, but is having trouble figuring out how to start with the parabola. They have been told that the problem might be related to the famous problem of the Brachistochrone curve, but they need to find a physics teacher to help them with the translation. They have been told that the solution to the brachistochrone is the cycloid, but they need to fit it to the points they have.
  • #1
Barioth
49
0
Hi, I'm trying to find the Acceleration of a ball rolling down on a parabola.


If I could find it, then I could integrate it twice and find it's parametric equation given by the time.
How could I find this?
I tried a few things, but nothing that made any sense.
If someone could give me a hint on where to start it would be super!


Thanks for passing by!
 
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  • #2
A couple of questions:

1. Do you have the equation for the parabola?

2. Are you ignoring rotational kinetic energy or not?

3. What is the radius of the ball?
 
  • #3
Sorry I should have given more information!

1- The equation is given but is variating, so I have to find a solution for its general form.

2- We're ignoring pretty much everything except gravity.

3-Since we're ignoring everything the radius isn't told.
 
  • #4
Barioth said:
Sorry I should have given more information!

1- The equation is given but is variating, so I have to find a solution for its general form.

2- We're ignoring pretty much everything except gravity.

3-Since we're ignoring everything the radius isn't told.

That helps, but I still don't know a few things. Is the parabola opening up? Down? What general form are you given? It might be helpful if you could state the original problem verbatim.
 
  • #5
I need to code in maple an animation of a ball rolling down multiple parabola and a straight line.

To find the fastest way for a ball to move from Point A to B.
They all start at the Point (0,0) and end at (K,-1)

K is given by the user before computing. I have 2 different parabola that have some difference in their acceleration.

I've managed to evalute r(t) for the straight line, but I can't figure out how to start with the parabola.
If I have \(\displaystyle y=ax^2+bx+c\) ( in my case C always equal to 0)

edit: I had guess it is opening up also.

The problem is in French and I'm doing my best to translate it, hope it sounds fine!
 
  • #7
Nice call MarkFL it is indeed!

I've managed to deal with the Brachistochrone ( Well I've found some equation that I had to change a litle bit to make it work for me...), but the parabola give me problem.

I might try to go find a physics teacher in my old school, I'm having an hard time translating the question.
 
  • #8
The solution to the brachistochrone (from the Greek for "shortest time") is the cycloid. To prove that requires the calculus of variations, and some technical details. Can you fit a cycloid to the points you have?
 
  • #9
Hi, I have solved the cycloide already, (I had to do my semester research on cycloide 3 years ago). I can make it fit the point that are given.

I'll put the parabola on the ice and do some reading, I might need some more knowledge
now!

Thanks for Helping Ackbach!
 

FAQ: Acceleration ball rolling on a parabola

What is the concept of "Acceleration ball rolling on a parabola"?

The concept of "Acceleration ball rolling on a parabola" refers to the motion of a ball rolling along a curved surface that follows the shape of a parabola. The ball experiences changes in velocity and acceleration as it moves along the parabola due to the force of gravity.

What factors affect the acceleration of a ball rolling on a parabola?

The acceleration of a ball rolling on a parabola is affected by several factors, including the angle of the parabola, the mass of the ball, and the force of gravity. The steeper the angle of the parabola, the greater the acceleration of the ball. A heavier ball will also experience greater acceleration, while the force of gravity remains constant.

How is the acceleration of a ball rolling on a parabola calculated?

The acceleration of a ball rolling on a parabola can be calculated using the equation a = g sinθ, where a is the acceleration, g is the force of gravity, and θ is the angle of the parabola. This equation takes into account the effect of gravity on the ball as it rolls along the curved surface.

What is the relationship between velocity and acceleration for a ball rolling on a parabola?

The relationship between velocity and acceleration for a ball rolling on a parabola is that the acceleration is directly proportional to the change in velocity. This means that as the ball accelerates or decelerates along the parabola, its velocity will also change accordingly.

What real-life applications involve the concept of "Acceleration ball rolling on a parabola"?

One real-life application of the concept of "Acceleration ball rolling on a parabola" is in the design of roller coasters. The tracks of roller coasters often follow the shape of a parabola, and the acceleration of the cars as they move along the track is calculated to provide a thrilling and safe ride for passengers. This concept is also used in sports, such as skiing and snowboarding, where athletes use the forces of gravity and the shape of the terrain to accelerate and control their movements.

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