Potential energy graph x-component

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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 point of equilibrium. To find the force at x=5, 25, and 35 cm, one must calculate the slope of the potential energy graph at those points. A positive slope indicates increasing potential energy, while a negative slope indicates decreasing potential energy. Understanding these concepts is crucial for analyzing forces in one-dimensional motion.
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:
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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