How Does the Force on a Particle Change with Position in a Potential Well?

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The discussion revolves around calculating the force on a particle in a potential well defined by the equation U(x) = 1.8x² - 4.5 J. The participant initially differentiated the potential energy function to find the force, resulting in F(x) = 3.6x, but encountered issues with the calculations at specific positions. They correctly identified that at x = 0 m, the force should be zero, but expressed confusion over the division by zero. Ultimately, the participant realized their initial calculations were correct but had made an error in significant figures when submitting their answers. The thread highlights the importance of careful calculation and attention to detail in physics problems.
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Homework Statement


A particle is trapped in a potential well described by U(x)= 1.8 x²-b where U is in joules, x is in meters, and b = 4.5 J.

Find the force on the particle when it's at x = 2.8m
Find the force on the particle when it's at x = 0 m
Find the force on the particle when it's at x = -1.4 m.

Homework Equations



F(x) = -dU(x) / dx

The Attempt at a Solution



so I just differentiated U(x), slapped a negative sign, and ended up with F(x) = 3.6x

Plugged in 2.8m, ended up with -10.08, and it ain't right. Any ideas why? I'm thinking it might have to do with the phrase "potential well".
 
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Never mind :blushing:

F(x) = U(x) / x

edit: (never mind)² by using this, part B came out correct, (the answer would be zero), but it doesn't make sense. By plugging zero in there, you're dividing by zero, which is ILLEGAL. so i guess I am back here for help, lol.

edit: (never mind)³ /sigh the way i had it originally was correct, but online I put in the wrong number of significant figures. oh well.
 
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