Question

A 100 lb cylinder is released from rest when h=0. Each spring has a stiffness of k=20 lb/ft

and an unstretched length of 2 ft. Using the principle of Conservation of Energy, determine the speed of the cylinder when h=3 ft.

Answer 1

The principle of Conservation of Energy is applied to a mechanical system of a cylinder and springs, where the initial potential energy of the compressed springs is converted into kinetic energy as the cylinder descends.

Step-by-step explanation:

The problem provided relates to the Conservation of Energy in a mechanical system consisting of a cylinder and springs, more specifically within the realm of classical mechanics. The Conservation of Energy principle states that the total energy of an isolated system remains constant if the system is subject to conservative forces. In this scenario, we ignore non-conservative forces such as friction.

When the cylinder is released from rest with a height h of 0, all the energy in the system is potential energy due to the springs' compression from their unstretched length. As the cylinder descends to h = 3 ft, the potential energy is converted into kinetic energy. The initial potential energy stored in the springs (since both springs are compressed by the same amount) is given by PE = 2(1/2)kx2, where k is the stiffness of the springs and x is the compression from the unstretched length. When the potential energy is fully converted into kinetic energy (KE = 1/2mv2), the principle of Conservation of Energy can be expressed as follows: PE_initial = KE_final.

Without the specific values such as the compression of the springs, the solution will be a general equation representing the final speed of the cylinder in terms of the known variables and assuming the springs were initially compressed.