Force and potential energy function

In summary, the conversation discusses a single conservative force acting on a particle within a system and the associated potential energy function. The potential energy function is calculated using the given values and variables. In part B, the change in potential energy and kinetic energy are calculated for a specific movement of the particle. The correct answers for part A and B are (A-5Bx^4)i and 977J, respectively.
  • #1
bdh2991
103
0

Homework Statement



A single conservative force acting on a particle within a system varies as = (− Ax + Bx5) N, where A and B are constants, is in Newtons, and x is in meters.

(a) Calculate the potential energy function U(x) associated with this force, taking U = 0 at x = 0. (Use any variable or symbol stated above as necessary.)
U(x) =



(b) Find the change in potential energy and change in kinetic energy as the particle moves from x = 1.90 m to x = 3.80 m. (Use any variable or symbol stated above as necessary.)



Homework Equations



F = -∇U



The Attempt at a Solution



for part a i took the partial derivative with respect to x in order to get the potential energy function in which i got the answer: U(x) = (A - 5Bx^4)i the system said it was wrong though.


for part b i took my equation in part a to find the change in potential energy and got -977J
and i figured if the change in potential was lost 977 J then the change in kinetic energy would have to be gaining 977 Joules, but i was wrong again. please help
 
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  • #2
Nvm i was doing it backwards and should have been integrating sorry guys
 
  • #3
what was the answer

what was the answer to part A
 

What is force?

Force is a physical quantity that describes the strength or intensity of a push or pull on an object. It is measured in units of Newtons (N).

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 a form of stored energy that can be converted into other forms, such as kinetic energy, when the object is in motion.

How are force and potential energy related?

Force and potential energy are related through the concept of work. When a force acts on an object and causes it to move a certain distance, work is done. This work is equal to the change in potential energy of the object. In other words, the force applied to an object can change its potential energy.

What is a force and potential energy function?

A force and potential energy function is a mathematical representation of the relationship between force and potential energy. It describes how the force acting on an object changes as the object's potential energy changes. This function is often used in physics calculations and can vary depending on the specific situation.

How can a force and potential energy function be calculated?

A force and potential energy function can be calculated using the fundamental principles of physics, such as Newton's laws of motion and the law of conservation of energy. It may also involve other variables such as distance, mass, and acceleration. Depending on the situation, different equations and methods may be used to calculate the force and potential energy function.

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