Calculating Work of Force Field F(x,y) on Particle Moving Along Parabola y=x²

Thread starter Caligula
Start date Jul 28, 2003
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Fields Force Force fields

In summary, when calculating the work of a force field on a particle moving along the parabola y=x², the work is equal to the integral of the force field F(x,y) multiplied by the displacement along the parabola, which is represented by ds = √(1+4x²)dx. This integral can be solved by using the substitution method and determining the limits of integration based on the starting and ending points of the particle's motion. The resulting value of the integral represents the work done by the force field on the particle as it moves along the parabola.

Jul 28, 2003

Caligula

Dose someone know how to do this...

Find the work done by the force field F(x,y) = x sin j + yj on particle that moves along the parabola y = x² from (-1,1) to (2,4).

With thanks,
Alex

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Jul 28, 2003

meteor

Just do a line integral along the parabola

1. How do you calculate the work of a force field on a particle moving along a parabola?

To calculate the work of a force field on a particle moving along a parabola, you will need to use the formula W = ∫F(x,y)·dr, where F(x,y) is the force field and dr is the displacement of the particle along the parabola. This integral can be solved by breaking it into smaller integrals and using the fundamental theorem of calculus.

2. What is the relationship between the force field and the parabola in this scenario?

The parabola represents the path along which the particle is moving, while the force field represents the forces acting on the particle at any given point on the parabola. The force field may vary in magnitude and direction at different points on the parabola.

3. How does the direction of the force field affect the work done on the particle?

The direction of the force field is important because it determines the angle between the force and the displacement of the particle. If the force and displacement are in the same direction, then the work done will be positive. If they are in opposite directions, the work done will be negative.

4. Can the work of a force field on a particle moving along a parabola ever be zero?

Yes, it is possible for the work of a force field on a particle moving along a parabola to be zero. This would occur if the force field is perpendicular to the displacement of the particle, resulting in a dot product of zero and thus no work being done.

5. Are there any other factors that need to be considered when calculating the work of a force field on a particle moving along a parabola?

Yes, in addition to the force field and the path of the particle, the mass of the particle also needs to be taken into account. This is because the work done is equal to the product of the force and the displacement, which is also equal to the change in kinetic energy of the particle. Therefore, a heavier particle will require more work to move along the same parabola compared to a lighter particle.