A small block with mass 0.0400 kg is moving in the ry-plane. The net force on the block is described by the potential-energy function U(x, y) = (5.50 J/m²)æ² – (3.60 J/m²)y³.

A hurricane wind blows across a 8m x 17m flat roof at a speed of 135  km/h.  Calculate the force exerted on the roof.  Hint:  The thickness of the roof is small, so the change in potential energy between the inside of the house and the outside can be approximated to be zero.  ρair  =1. 28 kg/ m3 .

Protons and neutrons (together called nucleons) are held together in the nucleus of an atom by a force called the strong force. At very small separations, the strong force between two nucleons is larger than the repulsive electrical force between two protons--hence its name. But the strong force quickly weakens as the distance between the protons increases. A well-established model for the potential energy of two nucleons interacting via the strong force is U=U0[1−e−x/x0] where x is the distance between the centers of the two nucleons, x0 is a constant having the value x0 = 2.0 × 10−15 m, and U0 = 6.0 × 10−11 J. Quantum effects are essential for a proper understanding of nucleons, but let us innocently consider two neutrons as if they were small, hard, electrically neutral spheres of mass 1.67 ×10−27 kg and diameter 1.0 × 10−15 m. Suppose you hold two neutrons 9.0 × 10−15 m apart, measured between their centers, then release them.What is the speed of each neutron as they crash…

Needs Complete typed solution with 100 % accuracy.

Problem 4: A 2.00 kg object moving in the x-y plane is under the influence of a force describe by the potential energy U (x,y) = (4.00 J/m³)x3 – (2.00 J/m4)y“. What is the magnitude and direction (angle) of the acceleration of the object at a point x=1 m and y = 2 m?

If the potential energy of a particle is given by U (r, y, 2) = –kry?2³, find the force associated with this potential energy where k is a positive constant. k(2x²yz³i+y²z³j + xy²2²k) kry²2*(i + ĵ + k) k(y²2³i + 2xyz³j + 3xy²2²k) -kry 2*(i +j+ k) 33 3 k(y²2*i+ xyz°j +xy²2² k)

An object moves in the x-y plane while acted on by the force F(x,y) = k1yi + k2xj, where k1 and k2 are constants with units of N/m. The object moves along a straight line path from Cartesian coordinate (x1, y1) to (x2, y2). Write an expression for the work done on the object by this force.