Final answer:
The mass-spring system described is a physics problem involving the calculation of potential and kinetic energies during simple harmonic motion. The questions pertain to finding potential energy at release, speed at equilibrium, and speed after travelling a certain distance.
Step-by-step explanation:
In considering a mass-spring system on a frictionless horizontal surface, you have a mechanical system with a mass m attached to a spring with stiffness k. Such a system is ideal for studying simple harmonic motion (SHM), where the mass oscillates back and forth due to the restoring force of the spring. Given the conditions of no external forces like friction or gravity doing work on the system, the system's total mechanical energy remains constant. The potential energy of the system in terms of displacement x from equilibrium can be described using the equation U(x) = 1⁄2kx².
Now let's specifically address a problem statement involving simple harmonic motion: A mass of 300g is attached to a spring with a spring constant of 100 N/m. When the mass is compressed 12 cm and released from rest, we want to determine (a) the potential energy stored at the moment of release, (b) the speed of the mass at the equilibrium point, and (c) the speed after it has traveled 20 cm from the release point.
- To find the potential energy at release, use U = 1⁄2kx², with k = 100 N/m and x = 0.12 m.
- The speed of the mass at the equilibrium point can be found using conservation of energy, converting all potential energy into kinetic energy KE = 1⁄2mv².
- The speed after traveling 20 cm requires calculating the potential energy at that point and using conservation of energy to find the remaining kinetic energy.