ball of mass m = 2kg is attached between two identical springs on a horizontal, frictionless tabletop. Both springs have spring constant k and are initially unstressed, and the particle is at x = 0. A) Draw the system. Represent the distance from the ball to the end of each spring as the variable L. This distance is the same for each spring as the ball is at an equilibrium position between the two springs. B) The ball is pulled a distance x along a direction perpendicular to the initial configuration of the springs as shown in the figure. Show that the force exerted by the springs on the particle is: Some formulas that needed to prove are in the picture
1 Work and Energy A ball of mass m = 2kg is attached between two identical springs on a horizontal, frictionless tabletop. Both springs have spring constant k and are initially unstressed, and the particle is at x = 0. A Draw the system. Represent the distance from the ball to the end of each spring as the variable L. This distance is the same for each spring as the ball is at an equilibrium position between the two springs. B The ball is pulled a distance x along a direction perpendicular to the initial configuration of the springs as shown in the figure. Show that the force exerted by the springs on the particle is: L F = -2kx1 - x2 + (1) Show that the potential energy of the system is given by the following equation: U = kx2 + 2kL(L - x2 + L2 (2)