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PE Diagram

Potential ene...

Question

Potential energy of a particle is given by $U = (2 - 3 x - 4 x^{2}) J$ where ' $x$ ' is in ' $m$ '. Find the magnitude of force at $x = 4 m$ , if the particle is free to move along $x$ -direction.

29 N

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35 N

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16 N

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18 N

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Solution

The correct option is B $35 N$
We know that, If the potential energy function $U (x)$ is known, then the force at any position can be obtained by taking the derivative of the potential

$\Rightarrow F = - \frac{\partial U}{\partial x}$
$= - \frac{\partial}{\partial x} (2 - 3 x - 4 x^{2})$
$= 8 x + 3 |_{x = 4 m}$
= $32 + 3$
$F = 35 N$

Hence option B is the correct answer

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Similar questions

Q. Potential energy of a particle is given by

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Potential energy of a particle is given by U=(2−3x−4x2) J where 'x' is in 'm'. Find the magnitude of force at x=4 m, if the particle is free to move along x-direction.

The correct option is B 35 NWe know that, If the potential energy function U(x) is known, then the force at any position can be obtained by taking the derivative of the potential ⇒F=−∂U∂x =−∂∂x(2−3x−4x2) =8x+3|x=4m = 32+3 F=35 N Hence option B is the correct answer

Potential energy of a particle is given by $U = (2 - 3 x - 4 x^{2}) J$ where ' $x$ ' is in ' $m$ '. Find the magnitude of force at $x = 4 m$ , if the particle is free to move along $x$ -direction.