Question

A 0.20 kg particle moves along the x axis under the influence of a stationary object. The potential energy is given by U(x) = 8x2 + 2x4, where U is in joules and x is in meters. If the particle has a speed of 5.0 m/s when it is at x = 1.0 m, its speed when it is at the origin is:

Answer 1

Answer:11.18 m/s

Explanation:

Given

mass of particle m=0.2 kg

Potential Energy U(x) is given by

$U(x)=8x^2+2x^4$

at x=1 m

$U(1)=8+2=10 J$

kinetic energy at x=1 m

$K.E.=\frac{1}{2}mv^2=\frac{1}{2}\times 0.2\times 5^2$

$K.E.=2.5 J$

Total Energy =U+K.E.

$Total=10+2.5=12.5 J$

at x=0, U(0)=0

as total Energy is conserved therefore K.E. at x=0 is equal to Total Energy

$\frac{1}{2}\times 0.2\times v^2=12.5$

$v^2=125$

$v=\sqrt{125}$

$v=11.18 m/s$