Introduction and Theory:
Collisions are essential in understanding how objects interact with each other. Conservation laws help us
predict the behavior of colliding objects without knowing every detail of the interaction. In this lab, we
will demonstrate that momentum is always conserved when no net external force is acting on a system,
while energy is conserved only in certain types of collisions. These principles have practical applications
in studying car crashes, planetary motion, and subatomic particle collisions.
We will be investigating one-dimensional collisions where the motion of objects is restricted to a
horizontal track. We will focus on two types of collisions: elastic and inelastic. In elastic collisions, kinetic
energy is conserved, while in inelastic collisions, kinetic energy is not conserved.
Objectives:
Our goal is to investigate simple elastic and inelastic collisions in one dimension, focusing on the
conservation of momentum and energy principles.
Equipment:
We will be using the VirtualPhysicsLabs environment, which includes a dynamics track, two carts, a set of
masses, and an ultrasonic motion sensor to record the position of the carts as a function of time.
LoggerPro software will be used for data analysis.
Procedure:
We will analyze five different collision cases in the VirtualPhysicsLabs environment. For each case, we will
record the masses of the two carts, their initial and final velocities, the momentum and kinetic energy of
each cart before and after the collision, and the total momentum and kinetic energy of the system
before and after the collision.
We will calculate the fractional change in momentum and kinetic energy for each case and determine
whether momentum and kinetic energy are conserved in each collision. We will also compare our results
to the theoretical predictions from the conservation laws.
Data Analysis:
Based on the cacluations, we will analyze the five collision cases and calculate the momentum, kinetic
energy, and their respective changes in each case.
Collision Case 1: Elastic Collision
Mass1: 2 kg
Initial Velocity1: 3 m/s
Final Velocity1: 1 m/s
Mass2: 1 kg
Initial Velocity2: 0 m/s
Final Velocity2: 4 m/s
Momentum and Kinetic Energy Calculations:
Initial Momentum1: Mass1 * Initial Velocity1 = 2 kg * 3 m/s = 6 kgm/s
Final Momentum1: Mass1 * Final Velocity1 = 2 kg * 1 m/s = 2 kgm/s
Initial Momentum2: Mass2 * Initial Velocity2 = 1 kg * 0 m/s = 0 kgm/s
Final Momentum2: Mass2 * Final Velocity2 = 1 kg * 4 m/s = 4 kgm/s
Initial Total Momentum: 6 kgm/s
Final Total Momentum: 6 kgm/s
Initial Kinetic Energy1: 0.5 * Mass1 * (Initial Velocity1)^2 = 0.5 * 2 kg * (3 m/s)^2 = 9 J
Final Kinetic Energy1: 0.5 * Mass1 * (Final Velocity1)^2 = 0.5 * 2 kg * (1 m/s)^2 = 1 J
Initial Kinetic Energy2: 0.5 * Mass2 * (Initial Velocity2)^2 = 0.5 * 1 kg * (0 m/s)^2 = 0 J
Final Kinetic Energy2: 0.5 * Mass2 * (Final Velocity2)^2 = 0.5 * 1 kg * (4 m/s)^2 = 8 J
Initial Total Kinetic Energy: 9 J
Final Total Kinetic Energy: 9 J
In this elastic collision, both the momentum and kinetic energy are conserved.
Collision Case 2: Inelastic Collision
Mass1: 2 kg
Initial Velocity1: 2 m/s
Final Velocity1: 1.333 m/s
Mass2: 1 kg
Initial Velocity2: 0 m/s
Final Velocity2: 1.333 m/s
Momentum and Kinetic Energy Calculations:
Initial Momentum1: Mass1 * Initial Velocity1 = 2 kg * 2 m/s = 4 kgm/s
Final Momentum1: Mass1 * Final Velocity1 = 2 kg * 1.333 m/s = 2.666 kgm/s
Initial Momentum2: Mass2 * Initial Velocity2 = 1 kg * 0 m/s = 0 kgm/s
Final Momentum2: Mass2 * Final Velocity2 = 1 kg * 1.333 m/s = 1.333 kgm/s
Initial Total Momentum: 4 kgm/s
Final Total Momentum: 4 kgm/s
Initial Kinetic Energy1: 0.5 * Mass1 * (Initial Velocity1)^2 = 0.5 * 2 kg * (2 m/s)^2 = 4 J
Final Kinetic Energy1: 0.5 * Mass1 * (Final Velocity1)^2 = 0.5 * 2 kg * (1.333 m/s)^2 ≈ 1.777 J
Initial Kinetic Energy2: 0.5 * Mass2 * (Initial VelocityEnergy2)^2 = 0.5 * 1 kg * (0 m/s)^2 = 0 J
Final Kinetic Energy2: 0.5 * Mass2 * (Final Velocity2)^2 = 0.5 * 1 kg * (1.333 m/s)^2 ≈ 0.888 J
Initial Total Kinetic Energy: 4 J
Final Total Kinetic Energy: ≈ 2.665 J
In this inelastic collision, momentum is conserved, but kinetic energy is not.
Collision Case 3: Perfectly Inelastic Collision
Mass1: 2 kg
Initial Velocity1: 1 m/s
Final Velocity1: 0.666 m/s
Mass2: 1 kg
Initial Velocity2: 0 m/s
Final Velocity2: 0.666 m/s
Momentum and Kinetic Energy Calculations:
Initial Momentum1: Mass1 * Initial Velocity1 = 2 kg * 1 m/s = 2 kgm/s
Final Momentum1: Mass1 * Final Velocity1 = 2 kg * 0.666 m/s = 1.332 kgm/s
Initial Momentum2: Mass2 * Initial Velocity2 = 1 kg * 0 m/s = 0 kgm/s
Final Momentum2: Mass2 * Final Velocity2 = 1 kg * 0.666 m/s = 0.666 kgm/s
Initial Total Momentum: 2 kgm/s
Final Total Momentum: 1.998 kgm/s (approximately 2 kg*m/s due to rounding)
Initial Kinetic Energy1: 0.5 * Mass1 * (Initial Velocity1)^2 = 0.5 * 2 kg * (1 m/s)^2 = 1 J
Final Kinetic Energy1: 0.5 * Mass1 * (Final Velocity1)^2 = 0.5 * 2 kg * (0.666 m/s)^2 ≈ 0.444 J
Initial Kinetic Energy2: 0.5 * Mass2 * (Initial Velocity2)^2 = 0.5 * 1 kg * (0 m/s)^2 = 0 J
Final Kinetic Energy2: 0.5 * Mass2 * (Final Velocity2)^2 = 0.5 * 1 kg * (0.666 m/s)^2 ≈ 0.222 J
Initial Total Kinetic Energy: 1 J
Final Total Kinetic Energy: ≈ 0.666 J
In this perfectly inelastic collision, momentum is conserved, but kinetic energy is not.
Collision Case 4:
Mass1: 3 kg
Initial Velocity1: 1 m/s
Final Velocity1: 0.5 m/s
Mass2: 2 kg
Initial Velocity2: 2 m/s
Final Velocity2: 1.5 m/s
Momentum and Kinetic Energy Calculations:
Initial Momentum1: Mass1 * Initial Velocity1 = 3 kg * 1 m/s = 3 kgm/s
Final Momentum1: Mass1 * Final Velocity1 = 3 kg * 0.5 m/s = 1.5 kgm/s
Initial Momentum2: Mass2 * Initial Velocity2 = 2 kg * 2 m/s = 4 kgm/s
Final Momentum2: Mass2 * Final Velocity2 = 2 kg * 1.5 m/s = 3 kgm/s
Initial Total Momentum: 7 kgm/s
Final Total Momentum: 4.5 kgm/s
0.5 * 3 kg * (1 m/s)^2 = 1.5 J
Final Kinetic Energy1: 0.5 * Mass1 * (Final Velocity1)^2 = 0.5 * 3 kg * (0.5 m/s)^2 = 0.375 J
Initial Kinetic Energy2: 0.5 * Mass2 * (Initial Velocity2)^2 = 0.5 * 2 kg * (2 m/s)^2 = 4 J
Final Kinetic Energy2: 0.5 * Mass2 * (Final Velocity2)^2 = 0.5 * 2 kg * (1.5 m/s)^2 = 2.25 J
Initial Total Kinetic Energy: 5.5 J
Final Total Kinetic Energy: 2.625 J
In this collision case, neither momentum nor kinetic energy is conserved.
0.5 * 3 kg * (1 m/s)^2 = 1.5 J
Final Kinetic Energy1: 0.5 * Mass1 * (Final Velocity1)^2 = 0.5 * 3 kg * (0.5 m/s)^2 = 0.375 J
Initial Kinetic Energy2: 0.5 * Mass2 * (Initial Velocity2)^2 = 0.5 * 2 kg * (2 m/s)^2 = 4 J
Final Kinetic Energy2: 0.5 * Mass2 * (Final Velocity2)^2 = 0.5 * 2 kg * (1.5 m/s)^2 = 2.25 J
Initial Total Kinetic Energy: 5.5 J
Final Total Kinetic Energy: 2.625 J
In this collision case, neither momentum nor kinetic energy is conserved.
Collision Case 5:
Mass1: 4 kg
Initial Velocity1: 2 m/s
Final Velocity1: 1.6 m/s
Mass2: 2 kg
Initial Velocity2: 0 m/s
Final Velocity2: 0.8 m/s
Momentum and Kinetic Energy Calculations:
Initial Momentum1: Mass1 * Initial Velocity1 = 4 kg * 2 m/s = 8 kgm/s
Final Momentum1: Mass1 * Final Velocity1 = 4 kg * 1.6 m/s = 6.4 kgm/s
Initial Momentum2: Mass2 * Initial Velocity2 = 2 kg * 0 m/s = 0 kgm/s
Final Momentum2: Mass2 * Final Velocity2 = 2 kg * 0.8 m/s = 1.6 kgm/s
Initial Total Momentum: 8 kgm/s
Final Total Momentum: 8 kgm/s
Initial Kinetic Energy1: 0.5 * Mass1 * (Initial Velocity1)^2 = 0.5 * 4 kg * (2 m/s)^2 = 8 J
Final Kinetic Energy1: 0.5 * Mass1 * (Final Velocity1)^2 = 0.5 * 4 kg * (1.6 m/s)^2 = 5.12 J
Initial Kinetic Energy2: 0.5 * Mass2 * (Initial Velocity2)^2 = 0.5 * 2 kg * (0 m/s)^2 = 0 J
Final Kinetic Energy2: 0.5 * Mass2 * (Final Velocity2)^2 = 0.5 * 2 kg * (0.8 m/s)^2 = 0.64 J
Initial Total Kinetic Energy: 8 J
Final Total Kinetic Energy: 5.76 J
In this collision case, momentum is conserved, but kinetic energy is not.
Conclusion:
Based on the data analysis of the five collision cases, we can conclude the following:
In elastic collisions (Case 1), both momentum and kinetic energy are conserved.
In inelastic collisions (Cases 2 and 3), momentum is conserved, but kinetic energy is not.
In certain collision scenarios (Cases 4 and 5), neither momentum nor kinetic energy may be conserved,
indicating possible discrepancies in the measured data or external forces affecting the system.