SUMMARY
The discussion centers on calculating the force constant k of a spring used to stop a subway train weighing 4.50 × 105 kg, initially traveling at 0.500 m/s over a distance of 0.900 m. The correct formula for k is derived from the relationship between kinetic energy and potential energy, specifically using k = mg/x. The initial kinetic energy (KE) of the train is calculated, and the potential energy (PE) of the spring is expressed as PE = (0.5)kx2. The correct value of k is determined to be 4900000 N/m.
PREREQUISITES
- Understanding of Newton's laws of motion
- Familiarity with the concepts of kinetic energy and potential energy
- Knowledge of spring mechanics and Hooke's Law
- Basic algebra for solving equations
NEXT STEPS
- Study the derivation of the spring constant using energy conservation principles
- Learn about Hooke's Law and its applications in mechanical systems
- Explore the relationship between kinetic energy and potential energy in dynamic systems
- Practice problems involving the calculation of spring constants in various scenarios
USEFUL FOR
Students studying physics, particularly those focusing on mechanics, as well as educators teaching concepts related to energy conservation and spring dynamics.