PHET Collision Lab We will be looking at a series of collisions using the simulation software at the web address (https://phet.colorado.edu/sims/html/collision-lab/latest/collision-lab_all.html). Go to the web address and click on the “Explore 1D” image to start the Ball Mass simulation. kg 0.5 Once loaded, click on the “More Data” button on the 1.5 bottom of the simulation. This will allow you to control positions, initial velocities, and masses. More Data Scenario #1: Elastic collisions between balls of equal mass with random initial velocities 1. We will look at three different completely elastic collisions. In each collision what do you expect to see in terms of momentum? Velocity Vectors Momentum Vectors Center of Mass | Momenta Diagram Kinetic Energy Show Values Elasticity 100% Inelastic Elastic 2. Fill in the table choosing different velocities for each object. Clicking on the “Show Values” option will allow you to get the velocities after the collision. Make sure to also de-select “Reflecting Border”. Reset All OSound Before Collision Velocity After Collision Velocity Mass Momentum Momentum 2 kg 1.5 m/s 2 kg 0 m/s Pi= Before Collision After Collision Mass Velocity Momentum Velocity Momentum 2 kg 1.5 m/s 2 kg -1.5 m/s Before Collision After Collision Mass Velocity Momentum Velocity Momentum 2 kg 3 m/s 2 kg 1 m/s
The Correct Answer and Explanation is :
In this simulation, we’re dealing with elastic collisions where two balls of equal mass collide. When it comes to elastic collisions, both momentum and kinetic energy are conserved. This means that after the collision, the total momentum of the system and the total kinetic energy of the system remain the same as they were before the collision.
Analysis of the provided scenario:
In the first part of the scenario, we have the following setup:
- Before Collision:
- Ball 1 (Mass = 2 kg, Velocity = 1.5 m/s)
- Ball 2 (Mass = 2 kg, Velocity = 0 m/s) Momentum before collision (Pi) for each ball:
- Ball 1: ( p_1 = m_1 \times v_1 = 2 \, \text{kg} \times 1.5 \, \text{m/s} = 3 \, \text{kg} \cdot \text{m/s} )
- Ball 2: ( p_2 = m_2 \times v_2 = 2 \, \text{kg} \times 0 \, \text{m/s} = 0 \, \text{kg} \cdot \text{m/s} ) Total Momentum before collision: ( P_{\text{total}} = 3 + 0 = 3 \, \text{kg} \cdot \text{m/s} )
- After Collision:
- Ball 1: ( v_1′ = -1.5 \, \text{m/s} )
- Ball 2: ( v_2′ = 1.5 \, \text{m/s} ) Momentum after collision (Pf) for each ball:
- Ball 1: ( p_1′ = m_1 \times v_1′ = 2 \, \text{kg} \times (-1.5 \, \text{m/s}) = -3 \, \text{kg} \cdot \text{m/s} )
- Ball 2: ( p_2′ = m_2 \times v_2′ = 2 \, \text{kg} \times 1.5 \, \text{m/s} = 3 \, \text{kg} \cdot \text{m/s} ) Total Momentum after collision: ( P_{\text{total}} = -3 + 3 = 3 \, \text{kg} \cdot \text{m/s} )
Momentum Conservation:
The total momentum before and after the collision is conserved at 3 kg·m/s, which is a fundamental principle of elastic collisions. This shows that the momentum of the system is unchanged by the collision.
Kinetic Energy Conservation:
The total kinetic energy is also conserved in elastic collisions. In this case, the kinetic energy before and after the collision should remain the same, demonstrating that no kinetic energy is lost in the collision, only transferred between the objects.
Elastic vs. Inelastic Collisions:
In this scenario, we have an elastic collision, where both momentum and kinetic energy are conserved. This contrasts with inelastic collisions, where momentum is conserved but kinetic energy is not—some of it is converted into other forms like heat, sound, or deformation.
This specific setup helps in demonstrating the key characteristics of elastic collisions, where after the interaction, the balls swap velocities, yet the total momentum and energy remain constant.