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
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