Ballistic Pendulum Lab Use this link to open the simulation for the Lab. file:///Users/zamiwilfriedjuniorbomisso/Downloads/BallisticPendulum04/index.html

The ballistic pendulum was invented by Benjamin Robins in 1742 as a device mainly designed to accurately measure the speed of fast traveling projectiles (bullets or cannon balls), relying only on measurements of mass and distance, without measurements of time. Knowing the mass of the projectile, estimates of its momentum and kinetic energy could also be made. Although the ballistic-pendulum method has lost its practical importance to more modern methodologies, it was used for a long time to advance the science of ballistics, and it is still useful today in classrooms to demonstrate basic properties of speed, momentum, and energy.

In the simplest configuration, a ballistic pendulum consists of a wooden block of mass mb suspended on a piece of string. A projectile of mass m is horizontally fired at the block and embeds itself in the block. This causes the combined block-plus-projectile system to swing up a height y. The initial speed of the projectile before it hits the block can be estimated using the expression

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The JavaScript provided with this document simulates a ballistic pendulum. It allows a user to change the initial speed of the projectileand the massesandof the projectile and the block, respectively. The simulation also shows the vertical coordinate y of the block as it is swinging up and down after the projectile collides with it (see the yellow box at the bottom right corner). Get familiar with running the simulation by changing the different available setting and controls and observe their effects.

1. Set the two masses to kg and kg and record the values in the data table below.

2. Run the simulation five times for different initial speeds of the projectile (ex. 150, 200, 250, 300, and 350 m/s).

3. For each step, record the initial speed of the projectile, the speed of the block-plus-projectile system right after the collision, and the maximum vertical coordinate y reached by the block as it swings up. Use the “step” button to run the simulation in small steps so you can read the changing values.

4. Calculate the initial speed using the expression and write it in the table.

5. Calculate the percentage difference in the initial speed and report it in the data table.

6. Calculate the initial momentum of the projectile before collision and the momentum of the block-plus-projectile system right after the collision and write the values in the table.

7. Calculate the percentage difference in momentum and report it in the table.

8. Calculate the initial kinetic-energy value of the projectile and the maximum gravitational potential energy of the block-plus-projectile system and write these in the table.

9. Calculate the percentage difference in energy and report it in the data table.

1. Is the initial kinetic energy of the projectile before collision equal to the maximum gravitational potential energy of the block-plus-projectile system after the collision? Elaborate by discussing the balance of energy in this process and the results you obtained from the data you collected.

1. Looking at the corresponding data in the table, how does the momentum of the projectile before collision compare to the momentum of the block-plus-projectile system after the collision? Justify your answer.

1. Show mathematically that the initial speed of the projectile before it hits the block is equal to

.

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