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A particle moves having a potential energy W(x)=4x^2-2x^4 Determine the acceleration...

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sapon | Student, Undergraduate | (Level 2) Honors

Posted March 21, 2011 at 1:54 AM via web

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A particle moves having a potential energy W(x)=4x^2-2x^4

Determine the acceleration of the particle at x=100m if the mass of the particle is 0.5 kg

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted March 21, 2011 at 1:59 AM (Answer #1)

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From Newton's second law, the acceleration is expressed as the ratio of the force and the unit mass.

F = m*dv/dt = m*a => a = F/m

Since we know the potential energy, we'll determine the intensity that is the same as acceleration.

We'll differentiate the expression of potential energy with respect to x.

dW/dx = d(4x^2-2x^4)/dx

dW/dx = 8x - 8x^3

Now, we'll substitute x by 100 m:

T = dW/dx

T = 8*100 - 8*100^3

T = 800(1 - 100^2)

T = 800(1 - 100)(1 + 100)

T = 800*99*101

T = a = 7999200 m/s^2

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