A particle is moving along the x-axis subject to the potential energy function

Click For Summary
To determine the x-component of the net force on a particle moving along the x-axis with the potential energy function U(x) = 1/x + x² + x - 1 at x = 3.67 m, the relationship between force and potential energy must be utilized. The net force can be found using the equation F(x) = -dU/dx, which requires calculating the derivative of the potential energy function. Attempts to integrate the potential energy function or directly substitute the position into the equation did not yield the correct force. Clarification on how to derive the force from the potential energy function is needed for a proper solution. Understanding the correct application of the derivative is essential for solving the problem.
AD_3
Messages
6
Reaction score
0

Homework Statement



A particle is moving along the x-axis subject to the potential energy function U(x) = 1/ x + x2 + x – 1. Determine the x-component of the net force on the particle at the coordinate x = 3.67 m.

Homework Equations


delta U=-∫F(x)*dx

The Attempt at a Solution


I tried to take the integral of the given function from 0 to 3.67 but that didn't work and I tried plugging in the the distance into the equation and that didn't work either.
 
Physics news on Phys.org
You need the force. How do you get force from potential?


ehild
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
View full post »

Similar threads

Is the line integral of tangential force in pendulum equal to the negative of change in potential energy?
  • · Replies 3 ·
Replies
3
Views
987
Time dependant Potential Energy in ion trap
  • · Replies 1 ·
Replies
1
Views
2K
Force components for mass attached to two springs
  • · Replies 15 ·
Replies
15
Views
1K
Particle moving from one potential to another
  • · Replies 13 ·
Replies
13
Views
1K
Exponential potential energy state diagram
  • · Replies 13 ·
Replies
13
Views
3K
Is potential energy defined only for internal conservative forces?
  • · Replies 15 ·
Replies
15
Views
2K
Misunderstanding of Gravitational Potential Energy
  • · Replies 7 ·
Replies
7
Views
3K
A rocket on a spring, related to potential/kinetic energy
  • · Replies 3 ·
Replies
3
Views
2K
Potential/Kinetic Energy of Particles in Harmonic Oscillator
  • · Replies 2 ·
Replies
2
Views
2K
Potential energy of a system of two punctual charges along the X axis
  • · Replies 7 ·
Replies
7
Views
1K