Potential energy functions of a particle

In summary, the given problem involves a single conservative force that varies as Fvec = (-Ax + Bx4)i N, where A and B are constants and x is in meters. The potential energy function U(x) associated with this force can be calculated as -1/2Ax2 + 1/5Bx5. From there, the change in potential energy and change in kinetic energy can be found using the given values and equations.
  • #1
ramenmeal
4
0

Homework Statement



A single conservative force acting on a particle varies as Fvec = (-Ax + Bx4)i N, where A and B are constants and x is in meters. Accurately round coefficients to three significant figures.
(a) Calculate the potential energy function U(x) associated with this force, taking U = 0 at x = 0. (Use A, B, and x as appropriate.)

(b) Find the change in potential energy and change in kinetic energy as the particle moves from x = 1.80 m to x = 3.40 m. (Use A, B, and x as appropriate.)

Homework Equations



w = f x d

The Attempt at a Solution



ive only attempted part a since i think i will need it to go on to part b.

w = f x d
f = (-Ax + Bx4)
d = x

PE = (-Ax + Bx^4)x = -Ax^2 + Bx^5
 
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  • #2
Since the force is continuously variable over the range of x isn't your U(x) the integral of the Force F(x) and not just the product of x and F(x)?
 
  • #3
oh yeah.. so should it be

(-1/2)Ax^2 + (1/4)Bx^5 ?

i'm not sure what form my final answer should be.
 
  • #4
ramenmeal said:
oh yeah.. so should it be

(-1/2)Ax^2 + (1/4)Bx^5 ?

i'm not sure what form my final answer should be.

How about -1/2Ax2 + 1/5Bx5 instead?
 

1. What is potential energy?

Potential energy is the energy that a particle possesses due to its position or configuration in a system. It is a form of stored energy that can be released or converted into other forms of energy.

2. How is potential energy related to a particle's position?

Potential energy is directly related to a particle's position in a system. The potential energy of a particle increases as its position moves away from a reference point, and decreases as its position moves closer to the reference point.

3. What factors determine the potential energy of a particle?

The potential energy of a particle is determined by factors such as its mass, its distance from a reference point, and the forces acting on it in the system.

4. Can potential energy change?

Yes, potential energy can change. It can be converted into other forms of energy, such as kinetic energy, or it can be released through a change in position or configuration of the particle.

5. How is potential energy used in scientific research?

Potential energy is a key concept in various fields of science, such as physics, chemistry, and engineering. It is used to analyze and understand the behavior of particles and systems, and to make predictions about their motion and interactions.

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