Kevin Tran
Lab Partners: Kevin Nguyen, Jose Rodriguez
May 1st, 2017

Ballistic Pendulum

Purpose: To determine the firing speed of a ball from a spring-loaded gun.

Introduction: We have a ball with a mass of 7.64 grams that undergoes an inelastic collisions with a nylon block with a mass of 77.6 grams, which is being supported with vertical strings. After the ball collides with the nylon block, both will rise through some angle, which loses kinetic energy and gains potential energy. When the system reaches its maximum height, the kinetic energy will be zero. 

Below is the model that we used to determine our angles. We pulled on the cannon to give it some initial potential energy. Once we released the string, the cannon will uncompress and launch a ball into the nylon block. We repeated this process 5 times to get 5 different angles.

Data Collected:

Mass of ball: 0.00764 kg

Mass of Nylon block: 0.0776 kg

Trial 1- 20.5 degrees +/- 0.5 degrees

Trial 2- 20.5 degrees +/- 0.5 degrees

Trial 3- 19.5 degrees +/- 0.5 degrees

Trial 4- 19.5 degrees +/- 0.5 degrees

Trial 5- 20.5 degrees +/- 0.5 degrees

We will use 20.5 degrees +/- 0.5 degrees as an average of all 5 angles.

The first left half represents conservation of linear momentum in the initial and final stage. The right half represents conservation of energy. We set up an equation for momentum when the ball inelastically collides with the nylon block. We have two unknowns, the initial velocity (what we're looking for) and final velocity. In order to find final velocity, we go to our conservation of energy and create and expression for "final velocity(Vf). The final velocity of the momentum expression is equal to the initial velocity of kinetic energy; therefore, we can connect both equations together.


Since we have an equation to solve for initial velocity(firing speed), we find our values and plug them in.

We measured the length of the string of 0.205 m.

In order to find our "Hcm", we can calculate by H= L-Lcos(angle).

H = 0.205m - (0.205m)(cos20.5 degrees)= 0.013 m




When we plugged in our values into the equation that we created, we get a firing speed of 5.63 m/s.

Next, began the verification process. We sticked a piece of carbon paper onto another piece of paper on the ground, which is where we expected the ball to land.

First, we measured the height from the ground to the center of the ball. As a result, the height is 0.976 m, and the height from the ground to the tip of the table is 0.895 m.

Next, we need to find the distance from the table to the spot where the ball landed on the carbon paper. In order to find the origin in where to start measuring, we used a string in order to get the best starting point to measure. 

Then, we used a two meter stick and an additional ruler to measure where the ball landed. We launched the ball three times and took the average distance that the ball lands. As a result, the distance from the table to the land is 2.144 m

Now, with the following data, we can use kinematics to solve for our velocity. In this case, we used two kinematics formulas to solve for this. (work shown below).


In comparison to the two velocities: 5.63 m/s and 4.8 m/s, the velocities are not the same but are close.

Conclusion: Overall, the types of errors that could occur within this lab is possibly air resistance when the ball is in mid air. Also, there could be friction within the nylon block that results us with different velocities when we performed the verification process. This lab allowed us to combined the conservation of linear momentum and conservation of energy to help us find our initial velocity/launch speed of the ball.