Lecture on Finding the Speed of a Bullet Using a Spring and Wooden Block

Key Concepts

• Objective: Determine the speed of a bullet using the properties of a spring and a wooden block.
• Components Involved:
  • Bullet
  • Wooden block
  • Spring

Experimental Setup

• Bullet Mass: 10 grams
• Block Mass (M): 5 kilograms
• Spring Compression: 10 centimeters (0.1 meters)
• Spring Constant (k): 200 Newtons per meter

Problem Breakdown

1. Collision

   • Type: Perfect Inelastic Collision
   • Conservation: Only momentum is conserved, not kinetic energy.
   • After collision: Bullet and block move together with a common velocity.

2. Energy Conservation

   • Kinetic energy from the bullet and block is converted into elastic potential energy of the spring.
   • Formulae:
     • Kinetic Energy: ( \frac{1}{2} MV^2 )
     • Elastic Potential Energy: ( \frac{1}{2} kX^2 )

Calculations

Step 1: Solve for Common Velocity (V)

• Formula: ( V = \sqrt{\frac{kX^2}{M + m}} )
• Given:
  • ( X = 0.1 ) meters
  • ( k = 200 ) Newton/meter
  • ( M = 5 ) kilograms
  • ( m = 0.01 ) kilograms
• Result: Calculate ( V ) for the block and bullet together.

Step 2: Use Momentum Conservation

• Before Collision:
  • Momentum of bullet = ( m \cdot v )
  • Momentum of block = 0 (stationary)
• After Collision:
  • Total Momentum = ( (M + m)V )
• Conservation Equation:
  • ( mv = (M + m)V )
• Solve for Bullet Velocity:
  • Result in velocity of bullet = 2000 m/s

Conclusion

• The speed of the bullet is determined using the compression of the spring and the properties of the system.
• Highlights importance of understanding both energy conservation and momentum conservation in solving physics problems.

Additional Information

• Encourage questions and discussions about the topic.
• Reminder to engage with the channel for further learning opportunities.