1. There are three ways to bring a 2.0 kg particle from the origin marked A (0, 5.0 m) C (5.0 m, 5.0 m) as (0,0) to point C with coordinates (5.0 m, 5.0 m) as shown in the accompanying diagram. Path 1 is along OAC, path 2 is along OBC, and path 3 is OC. Suppose that the force that will do this work has the following components: F. =4.0 N and F, =3.0 N. Find the work done by this force in each path. Is this force conservative? O (0, 0) B (5.0 m, 0) 2. Find the associated potential energy for the force exerted by an elastic spring.1. A 1.25 kg ball is projected vertically upward from the ground with an initial speed of 5.6 m's. (a) How high will it rise? (b) What is its speed when it is at half of its maximum height? Use conservation of mechanical energy to solve this problem. 2. A block of mass 2.25 kg starts out at rest at the top of a 15.0 m long plane inclined 30 with the horizontal. (a) What is its initial gravitational potential energy? As it slides down the plane, the block encounters a frictional force of 3.5 N. (b) How much work is done to overcome friction? (c) What is the kinetic energy of the block when it reaches the bottom of the incline? At a distance of 0.5 m from the bottom of the inclined plane is a horizontal spring of force constant 52 N/m. Suppose that the coefficient of kinetic friction between the block and the horizontal surface is 0.15. (d) What is the kinetic energy of the block just before it 150 m comes in contact with the spring? (c) By how much will the WW.0.5mi spring be compressed? (f) What is the work done against 130 friction as the block moves along the horizontal surface? What are the three types of equilibrium? When is mechanical energy conserved