Chapter 14: Problem 79
A spring of negligible mass and force constant \(k =\) 400 N/m is hung vertically, and a 0.200-kg pan is suspended from its lower end. A butcher drops a 2.2-kg steak onto the pan from a height of 0.40 m. The steak makes a totally inelastic collision with the pan and sets the system into vertical SHM. What are (a) the speed of the pan and steak immediately after the collision; (b) the amplitude of the subsequent motion; (c) the period of that motion?
Short Answer
Step by step solution
Determine Potential Energy of the Steak
Calculate Speed After Collision Using Energy Conservation
Use Conservation of Momentum for Speed After Collision
Determine Amplitude of Motion
Calculate Period of Simple Harmonic Motion
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Conservation of Energy
Key Points:
- Energy transitions within a system can be used to predict motion.
- Gravitational potential energy changes to kinetic energy during free fall.
- Post-collision energy is stored as elastic potential energy in the spring.
Momentum Conservation
Key Points:
- Momentum is conserved in isolated systems.
- Calculating post-collision velocities involve initial momentum considerations.
- This principle helps predict velocities and directions in collisions.
Mass-Spring System
Important Considerations:
- Mass-spring systems are ideal for studying simple harmonic motion.
- Understanding spring constant and mass helps predict oscillation characteristics.
- The system's energy alternates between kinetic and elastic potential.
Kinetic Energy
Key Insights:
- Kinetic energy represents motion within the system.
- The conversion from potential to kinetic energy is a key step in falling bodies.
- Post-collision, kinetic energy influences further motion characteristics.
Elastic Potential Energy
Key Elements:
- Elastic potential energy is stored when spring is compressed or stretched.
- The spring constant affects how much energy is stored.
- The energy contributes to restoring force, driving the system's motion.