Dick said:Yep, you got it set up all right. But I do get 972/5 for the double integral of 6*x^2*y^2 over the triangle. Check that again. Post how you worked it out if you can't get it.
The work done by a force field is the measure of energy transferred to an object as it moves through the field. It is the product of the force exerted on an object and the displacement of the object in the direction of the force.
The work done by a force field is calculated by multiplying the magnitude of the force by the displacement of the object in the direction of the force. Mathematically, it can be expressed as W = F * d * cosθ, where W is work, F is force, d is displacement, and θ is the angle between the force and displacement vectors.
Some common examples of force fields include gravitational fields, electric fields, magnetic fields, and frictional fields. These are all types of fields that exert a force on objects within their reach.
Yes, work done by a force field can be negative. This occurs when the force and displacement vectors are in opposite directions, resulting in a negative value for work. This indicates that energy is being taken away from the object instead of being transferred to it.
The work done by a force field is directly related to potential energy. As an object moves through a force field, the work done by the field is stored as potential energy in the object. This potential energy can be converted into kinetic energy as the object moves out of the field.