If the potential energy of the particle is given by: U = x2-8x+16. It starts from rest from x=0. What will be its maximum speed during SHM? Assume the mass of the particle to be 1kg.
If the potential energy of the particle is given by: U = x2-8x+16. It starts from rest from x=0. What will be its maximum speed during SHM? Assume the mass of the particle to be 1kg. Correct Answer 4√2m/s
F = -dU/dx = 8 – 2x. Particle starts from x=0, so force will increase its speed till force becomes zero at x=4. Let acceleration be ‘a’. a = dv/dt = v dv/dx. And a = F/m = F/1 = 8-2x. adx = vdv. Now, integrate both sides. The limits of dx will be 0 to 4 and the limits of dv will be 0 to v. (8x – x2)04 = v2/2. ∴ v = 4√2 m/s.
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Feb 20, 2025