Realistic Ballistic Pendulum

An interactive physics laboratory simulation.

Variables

Result

Max Height (h): 0.00 cm
Maximum Angle (θ): 0.00°
Initial Momentum (p): 0.00 kg·m/s
Initial K.E.: 0.00 J
Verified Velocity: 0.00 m/s
Experiment Details ▼

1. Aim of the Experiment

To verify that energy conservation and momentum conservation can be used with a ballistic pendulum to determine the initial velocity of a projectile, its momentum and kinetic energy.

2. Apparatus Required

Ballistic Pendulum (Bob suspended by a weightless string), Projectile Launcher, Projectile (Bullet), Protractor/Measuring Scale for angle and height.

3. Theory

The ballistic pendulum experiment is a classic physics problem that involves two key conservation principles:

  • Conservation of Linear Momentum: During the collision between the bullet and the pendulum block, the system is isolated. Since the collision is perfectly inelastic (the bullet embeds in the block), the total momentum of the system just before the collision is equal to the total momentum just after the collision.
  • Conservation of Mechanical Energy: After the collision, as the combined mass of the pendulum and bullet swings upwards, mechanical energy is conserved. The kinetic energy of the combined mass at the lowest point of the swing is converted into gravitational potential energy at the highest point of the swing.

4. Formulas Used

Momentum (p) = m × v

Kinetic Energy (K.E) = ½ × m × v²

Height (h) = L × (1 - cos(θ))

Bullet Velocity (v) = ((m+M)/m) × √(2gh)

5. Procedure

  1. Set Initial Conditions: Use the sliders and dropdown menu in the "Variables" panel to set the desired gravitational environment, bullet mass, pendulum mass, and initial bullet velocity.
  2. Fire the Projectile: Press the "Shoot" button. This will initiate the animation, showing the bullet traveling and colliding with the pendulum block.
  3. Observe the Swing: Watch as the pendulum, with the bullet embedded, swings upwards to its maximum height. The animation will pause at the peak of the swing before returning.
  4. Record the Results: Note the "Maximum Angle (θ)" and "Maximum Height (h)" displayed in the "Result" panel. These are the key outcomes of the swing.
  5. Verify the Velocity: Compare the initial "Bullet Velocity" you set with the "Verified Velocity" in the results. The "Verified Velocity" is calculated using the swing height (h). According to the conservation laws, these two values should be almost identical, confirming the theory.
  6. Repeat and Analyze: Press the "Reset" button. You can now change the parameters and run the experiment again to see how different masses, velocities, and gravity affect the outcome.