Potential energy graph x-component

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SUMMARY

The x-component of the force on a particle can be determined using the formula |F| = -dU/dx, where U represents potential energy. At x=15 cm, the force is zero, indicating a local extremum in potential energy. To find the x-component of the force at x=5, 25, and 35 cm, one must calculate the slope of the potential energy graph at these points. The slope indicates whether the potential energy is increasing or decreasing, thus determining the direction of the force.

PREREQUISITES
  • Understanding of potential energy (U) and its graphical representation
  • Knowledge of calculus, specifically differentiation
  • Familiarity with the concept of force in physics
  • Basic understanding of one-dimensional motion
NEXT STEPS
  • Study the relationship between force and potential energy in one dimension
  • Learn how to differentiate functions to find slopes
  • Explore the concept of gradients in three-dimensional potential energy fields
  • Practice problems involving the calculation of forces from potential energy graphs
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy concepts, as well as educators seeking to clarify the relationship between force and potential energy.

psingh
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What is the x-component of the force on the particle at x=5, 15, 25, and 35 cm

i thought it was just the slope?!? but I am wrong ,some help?

x=15 i know F=0
 

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psingh said:
What is the x-component of the force on the particle at x=5, 15, 25, and 35 cm

i thought it was just the slope?!? but I am wrong ,some help?

x=15 i know F=0


so close!

there's a formula that should be in your text:

|F| = - dU/dx. (direction is along the x-axis.)

(if, like in this problem, we are only concerned with one dimension.)

in three dimensions, F = - grad U
 
oye you're right neg. slope =] thankss
 
In differential form , the relation is fiven by

F = \frac{-dU}{dR}

Just find the slope of the tangents at each of the given x-coordinates . The answer will be positive or negative depending on whether Potential is decreasing or increasing at that point.

BJ
 
Last edited:

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