Function describing Potential Energy

In summary, the conversation is about a request for help with a problem involving an equation and the potential energy of a point mass. The function vector that describes the force on the object at different coordinates is being sought, using the equation ##F=-\nabla U##. The individual is looking for guidance on how to approach the problem and is asking if anyone can provide a hint or show their work to see where they may be going wrong.
  • #1
JC91
1
0
Hi, can someone please help me on this problem. I'm not sure what to do with the equation given. I tried taking the derivative, partial, and anti and nothing seems to be working. Can someone please give me a hint on how to start this problem.

Thanks in advance.

Suppose the following function describes the potential energy of a point mass (m=3 kg) at various locations in the xy plane:

U(x,y)=x2 - y2 + 32
(Units omitted; you may assume [x], [y] = m and = J.)

a.) Find a general function vector F(x,y) and then use it to find the force on the object at the following (x,y) coordinates:

vector F(+6 m,+1 m) = ___N i hat + ___N j hat

vector F(+6 m,-1 m) = ___N i hat + ___N j hat

vector F(-6 m,+1 m) = ___N i hat + ___N j hat

vector F(-6 m,-1 m) = ___N i hat + ___N j hat
 
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  • #2
Use the equation ##F=-\nabla U##. Maybe show us your work so we can see what's going wrong?
 

FAQ: Function describing Potential Energy

What is potential energy?

Potential energy is the energy that an object possesses due to its position or configuration in a force field. It is often described as the energy that is stored in an object.

How is potential energy related to the function describing it?

The function describing potential energy is a mathematical equation that helps us understand the relationship between an object's position and its potential energy. This function allows us to calculate the potential energy of an object at any given point in a force field.

What factors affect the function describing potential energy?

The function describing potential energy is affected by several factors such as the mass of the object, the strength of the force field, and the object's position in the force field. Other factors may also include the type of force (e.g. gravitational, electric) and the distance between interacting objects.

How is potential energy different from kinetic energy?

Potential energy is the energy that an object has due to its position, while kinetic energy is the energy an object possesses due to its motion. Both forms of energy are interconvertible, with potential energy being converted into kinetic energy as an object moves within a force field.

Why is the function describing potential energy important in scientific research?

The function describing potential energy is important in scientific research because it helps us understand the behavior of objects in a force field and predict their movements. This function is also used in various fields such as physics, chemistry, and engineering to solve problems and make predictions about the behavior of systems.

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