# Calculating Force Components for U = 7x^2 + 9xy + 3(y^2)z

• Stryder_SW
In summary, the question asks for the components of the force vector F given the equation U = 7x^2 + 9xy + 3(y^2)z. The attempted solution provided Fx=-14x-9y, Fy=-9x-6yz, and Fz=-3y^2. The poster is unsure about the correctness of Fx and plans to consult their professor for confirmation.
Stryder_SW

## Homework Statement

If U = 7x^2 + 9xy + 3(y^2)z, what are the components of the force vector F ?

## The Attempt at a Solution

These are the answers I've come up with. I've gotten Fy and Fz correct, but the Fx is wrong and I'm pretty sure its actually right. However, I would love to be proven wrong lol.
Fx=-14x-9y
Fy=-9x-6yz
Fz=-3y^2

Welcome to PF!

Hi Stryder_SW! Welcome to PF!
Stryder_SW said:
If U = 7x^2 + 9xy + 3(y^2)z, what are the components of the force vector F ?

Fx=-14x-9y
Fy=-9x-6yz
Fz=-3y^2

Well, your Fx looks right to me.

yeah, I'm about to message my professor lol.

## 1. What is the relationship between force and potential energy?

Force and potential energy are directly related. The force acting on an object is equal to the negative gradient of its potential energy. This means that as potential energy increases, the force acting on the object also increases.

## 2. How do we determine force from potential energy?

To determine the force acting on an object from its potential energy, we can use the equation F = -dU/dx, where F is the force, U is the potential energy, and x is the position of the object. This equation is derived from the relationship between force and potential energy.

## 3. Can force and potential energy be negative?

Yes, both force and potential energy can be negative. This indicates that the force is acting in the opposite direction of the object's motion, and that the potential energy is decreasing as the object moves in that direction.

## 4. What is the unit of force and potential energy?

The standard unit of force is Newtons (N), while the unit of potential energy is Joules (J). However, in some cases, different units may be used, such as pound-force (lbf) for force and foot-pounds (ft-lbf) for potential energy.

## 5. How does the direction of the force affect potential energy?

The direction of the force affects potential energy in two ways. First, a force acting in the same direction as an object's motion will increase its potential energy. Second, a force acting in the opposite direction of an object's motion will decrease its potential energy. This is because potential energy is a measure of the work done by a force on an object, and the direction of the force determines the direction of the work.

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