A force parallel to the x-axis acts on a particle moving along the x-axis. The force produces a potential energy U (x) given by U (x) = ↵x4, where ↵ = 0.630 J/m4. What is the force (magnitude and direction) when the particle is at x = 0.800 m?

The force acting on the particle at x = -0.800 has magnitude of 1.29 N and directed toward the origin

Explanation:

First we write the potential energy produced by the force

where α = 0.630

therefore

For motion along a straight line, a conservative force is the negative derivative of its associated potential energy function U(x):

therefore

At  x = -0.80 the force equals

what was the acceleration of the 2 kg cart?

⇒ 16.0 cm/s2

what was the acceleration of the 4 kg cart?

⇒ 8.1 cm/s2

what was the acceleration of the 6 kg cart?

⇒ 5.3 cm/s2

both the fifth and fourteenth amendments of the united states contain a due process clause. while the fifth amendment describes a legal obligation of the federal government to not deprived of life, liberty or property without due process of law, the fourteenth amendment applies the same obligation to the states to guarantee that all of the states provide fair procedures as well.