- #31
- 42,802
- 10,495
Neither do I, but don't tell anyone.erobz said:
A Stone connected to chain is thrown vertically
- Thread starter Rikudo
- Start date
Click For Summary
SUMMARY
The discussion centers on the dynamics of a stone connected to a chain thrown vertically, analyzing the forces and equations of motion involved. Key equations derived include Newton's second law for the stone, $$-F-mg=m \ddot h$$, and the impulse-momentum relationship $$\frac{dp}{dt} = F - \lambda gh$$. Participants debate the conservation of work and momentum, highlighting the complexities of chain dynamics and the potential loss of energy during motion. The final consensus suggests that the maximum height of the stone is influenced by both the initial speed and the length of the chain, with calculations indicating a maximum height of 40 m under specific conditions.
PREREQUISITES- Understanding of Newton's laws of motion
- Familiarity with impulse-momentum theory
- Basic knowledge of differential equations
- Concept of mechanical energy conservation
- Study the derivation of equations of motion for systems involving chains and ropes
- Explore the application of Lagrangian mechanics in complex motion problems
- Investigate the effects of energy loss in inelastic collisions
- Learn about dimensional analysis in physics problems
Physics students, mechanical engineers, and anyone interested in the dynamics of connected systems and energy conservation principles.