Lab : Ballistic Pendulum Simulation

Question

link simulation : https://ophysics.com/e3.html

Part I: Deciphering the initial velocity of the bullet from the maximum height of the

pendulum

In this part of the lab, you are going to calculate the initial velocity of the bullet given the

maximum height of the pendulum swing that you will be measuring with the simulation. You

are going to do this twice.

First, measure the maximum height with the bullet set to its minimum velocity setting. To do

this slide the setting for the Initial Velocity of the Bullet (m/s) to the farthest left position

possible. Set the mass of the bullet to 0.1kg and the mass of the block to 5kg. When you are

ready press “Fire”. Use the height slider to find the maximum height of the pendulum

measured from the height of the pendulum when it is not swinging before the bullet hits it.

Question 1: What did you measure for the maximum height of the pendulum during the swing

in meters? (Only input the number don’t include units)

Use Eq. III to find the initial velocity of the bullet for this set-up.

Question 2: What did you calculate the initial speed of the bullet to be in m/s? (Only input the

number as it is in [m/s])

Question 3: Toggle on the initial velocity in the simulation to find the theoretical value for the

initial velocity of the bullet. What is the percent error between your value and the given value

from the simulation (Only input the number in units of percent, do not include the % symbol)

Second, toggle the initial velocity off again and now measure the maximum height with the

bullet set to its maximum velocity setting. To do this slide the setting for the Initial Velocity of

the Bullet (m/s) to the farthest right position possible. Leave the mass of the bullet at 0.1kg and

the mass of the block at 5kg. When you are ready press “Fire”. Use the height slider to find

the maximum height of the pendulum measured from the height of the pendulum when it is not

swinging before the bullet hits it.

Question 4: What did you measure for the maximum height of the pendulum during the swing

in meters? (Only input the number don’t include units)

Use Eq. III to find the initial velocity of the bullet for this set-up.

Question 5: What did you calculate the initial speed of the bullet to be in m/s? (Only input the

number as it is in [m/s])

Question 6: Toggle on the initial velocity in the simulation to find the theoretical value for the

initial velocity of the bullet. What is the percent error between your value and the given value

from the simulation (Only input the number in units of percent, do not include the % symbol)

Answer 1

This is an example of a Conservation of Energy lab assignment.

When the bullet is sent flying with some initial horizontal velocity, it contains a certain amount of Kinetic Energy (the energy of any mass in motion) according to the formula KE = 1/2 m*v²

When the bullet strikes and is embedded in the ballistic pendulum, they combine and are treated as one mass. This is what we call a perfectly inelastic collision. An inelastic collision means that momentum is not conserved, but that's okay since momentum isn't what we're tracking in this lab. Energy of the bullet-pendulum system is conserved thanks to the Law of Conservation of Energy. Since the bullet and pendulum combined (m+M) have much greater mass than the bullet alone (m), we expect the velocity of the system to be proportionately smaller according to the formula

1/2 m*v₁²=1/2(m+M)*v₂²

As the pendulum swings upward, the initial kinetic energy of the system is changed into gravitational potential energy, the form of energy that object with mass acquire when they are moved up against the force of gravity. At the top of the pendulum's swing, all of the system's kinetic energy has been converted into gravitational potential energy. Since we can measure the change in elevation of the pendulum-bullet system (Δh), we can easily determine the final gravitational potential energy according to the formula

PE = (m+M)g*Δh

Since energy in this system is conserved (and there is no outside force acting to add or take away energy), we can set the final potential energy equal to the bullet's initial kinetic energy. As long as we know the mass of the bullet (m) and pendulum (M), the bullet-pendulum system's final height (Δh), and the acceleration due to gravity (g), we can solve for the bullet's initial velocity (v_i) through the following equation:

1/2 m*v_i² = (m+M)g*Δh

v_i² = 2(m+M)g*Δh/m

v_i = sqrt[2(m+M)g*Δh/m]

Differences between measured and theoretical answers to this problem may arise from energy loss due to air resistance on the bullet or friction in the pendulum, both of which represent not a violation of the Law of Conservation of Energy, but merely energy being transferred into less useful forms (airflow, heat) during the course of the experiment.