Reaction force on a semi-cubical parabola

In summary, the problem involves a particle moving along a semi-cubical parabolic curve with a constant speed v. The reaction force of the curve on the particle is given by F=mv^2/r, and in order to find the value of r, one must use the formula for radius of curvature of a curve. This can be found through further investigation or by using a ready-made formula.
  • #1
zorro
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Homework Statement



A particle of mass m moves without friction along a semi-cubical parabolic curve given by y2=4ax3 with a constant speed v. The reaction force of the curve on the particle when it is at the point (x = 1, y = 2) is given approximately by

The Attempt at a Solution



F=mv2/r

How do I find out 'r' here?
 
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  • #2
I suggest that the r value is the radius of curvature of the path on which the particle travels.
 
  • #3
I did not ask 'what does r stand for?'! :rolleyes:
 
  • #4
Have you investigated how to find the radius of curvature of a curve? There's a http://en.wikipedia.org/wiki/Radius_of_curvature_%28applications%29" that might shed some light.
 
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  • #5
Oh I see!...so there is a 'ready made' formula for that. Thanks!
 

FAQ: Reaction force on a semi-cubical parabola

What is a semi-cubical parabola?

A semi-cubical parabola is a three-dimensional shape that resembles a parabola cut in half. It has curved sides and a flat base.

How is the reaction force on a semi-cubical parabola calculated?

The reaction force on a semi-cubical parabola can be calculated using the formula F = ma, where F is the force, m is the mass of the object, and a is the acceleration. This formula is derived from Newton's second law of motion.

What factors affect the reaction force on a semi-cubical parabola?

The reaction force on a semi-cubical parabola can be affected by the mass of the object, the angle at which it is launched, and the force of gravity. Other factors such as air resistance and surface friction can also play a role.

How does the reaction force on a semi-cubical parabola change with different launch angles?

The reaction force on a semi-cubical parabola is highest when launched at a 45-degree angle. As the launch angle increases or decreases from this optimal angle, the reaction force decreases.

What real-life applications involve the use of reaction force on a semi-cubical parabola?

The concept of reaction force on a semi-cubical parabola is commonly used in sports, such as in the flight of a soccer ball or a basketball shot. It is also important in understanding the trajectory of projectiles in physics and engineering applications.

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