# Potential Energy - Potential function problem.

• Alpha Russ Omega
In summary, the problem is difficult to start, and a potential function is given which provides the acceleration of a 2 kg mass when at the position x = 0.2 m.
Alpha Russ Omega
Hello:
I'm having trouble starting a certain problem.

A potential function is given by U(x) = 12 x^2. What will be the acceleration (in meters/second ^2) of a 2 kg mass, when it is at the position x = 0.2 m?

Any help will be highly appreciated.

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How is the potential energy function related to the force? And in turn, how is force related to acceleration?

quasar987 said:
How is the potential energy function related to the force? And in turn, how is force related to acceleration?

Hmmm... Well, here is what I can think of from what I've learned in class:

1. The potential energy function is tied into a conservative force for x. Maybe I can go with the formula of: F cons. x = - ∂U/∂x
2. Force is related to acceleration by: F net = (mass) x (acceleration) Thus: *acceleration = (mass) / (F net)
Am I on the right track?

*EDIT: acceleration = (F net) / (mass)

Last edited:
Alpha Russ Omega said:
Hmmm... Well, here is what I can think of from what I've learned in class:

1. The potential energy function is tied into a conservative force for x. Maybe I can go with the formula of: F cons. x = - ∂U/∂x
2. Force is related to acceleration by: F net = (mass) x (acceleration) Thus: acceleration = (mass) / (F net)
Am I on the right track?

yes. now, put all the equations together and solve for acceleration.

Alrighty, so by taking the derivative of 12x^2 I get 24x. To get the Force would I multiply 0.2 meters by 24 ?

B.T.W.: (Thank you for all the replies.)

That's right.

not quite, but almost. you forgot the negative when calculating the force.

because acceleration does not equal mass/force (you still forgot the negative)

Oh my goodness! (brain fart) I see my mistake now. a = Fnet / mass
Thus being: (-4.8)/(2 kg) = -2.4 m/s^2

Thank you folks for all your help!

## 1. What is potential energy and how is it related to potential function?

Potential energy is the energy that an object possesses due to its position or configuration. Potential function is a mathematical representation of potential energy and is used to describe the energy of a system based on its position. The value of the potential function at a given point is equal to the potential energy at that point.

## 2. Can you provide an example of a potential function problem?

One example of a potential function problem is a mass attached to a spring. The potential function in this case would be given by the equation U(x) = (1/2)kx², where k is the spring constant and x is the displacement of the mass from its equilibrium position.

## 3. How is potential energy different from kinetic energy?

Potential energy is the energy an object has due to its position or configuration, whereas kinetic energy is the energy an object has due to its motion. Potential energy can be converted into kinetic energy and vice versa, depending on the system and its surroundings.

## 4. What factors affect potential energy in a system?

The factors that affect potential energy in a system include the mass of the object, the gravitational or electromagnetic forces acting on the object, and the position or configuration of the object within the system. Changes in any of these factors can result in a change in potential energy.

## 5. How is potential energy used in real-world applications?

Potential energy is used in a variety of real-world applications, such as energy storage systems like batteries and dams, as well as in the design of structures like roller coasters and bridges. Understanding potential energy can also help in predicting the behavior of objects in different environments, such as predicting the trajectory of a satellite in orbit.

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