Question

the objects change their speed or direction when they collide with each other or the borders of the collision area. however, their velocities remain unchanged as they move from one collision to the next. click on \more data\ above the mass values to view the velocity of each object. pause the simulation by clicking on the square counterclockwise button to the bottom right of the collision area (not the bottom right of the simulation). this will reset the positions of both objects while keeping their masses at 1.50 kg. click on the \slow\ setting below the collision area. then, observing the objects velocities, press play. pause the simulation after the objects collide, observing their new velocities. what are the velocities of each object before and after the collision? enter your answers in the boxes.
$v_{\text{i, object 1, initial}}$
$v_{\text{i, object 2, initial}}$
$v_{\text{f, object 1, final}}$
$v_{\text{f, object 2, final}}$

Explanation:

To solve this, we follow the simulation instructions:

Step 1: Set up the simulation

• Pause/reset the simulation (square counterclockwise button) to reset positions, masses = 1.50 kg.
• Select “Slow” setting below the collision area.

Step 2: Observe pre - collision velocities

• Press play, observe velocities of Object 1 (teal) and Object 2 (pink) before collision. From typical PhET Collision Lab (elastic collision, equal mass, initial setup: often \( v_{\text{Object 1, Initial}} = +1.00\ \text{m/s} \), \( v_{\text{Object 2, Initial}} = -1.00\ \text{m/s} \) or similar, but follow the simulation’s “More Data” for exact values).

Step 3: Observe post - collision velocities

• Pause after collision, observe new velocities. For equal - mass elastic collision, velocities swap: \( v_{\text{Object 1, Final}} = -1.00\ \text{m/s} \), \( v_{\text{Object 2, Final}} = +1.00\ \text{m/s} \) (matches conservation of momentum/kinetic energy for elastic, equal - mass collisions).

Example (Typical PhET Collision Lab Output):

• \( v_{\text{Object 1, Initial}} = 1.00\ \text{m/s} \)
• \( v_{\text{Object 2, Initial}} = -1.00\ \text{m/s} \)
• \( v_{\text{Object 1, Final}} = -1.00\ \text{m/s} \)
• \( v_{\text{Object 2, Final}} = 1.00\ \text{m/s} \)

(Note: Actual values depend on the simulation’s initial settings. Follow the “More Data” panel in the simulation to get precise velocity values.)

If we assume the standard equal - mass elastic collision setup:

Answer:

\( v_{\text{Object 1, Initial}} = \boldsymbol{1.00}\ \text{m/s} \)
\( v_{\text{Object 2, Initial}} = \boldsymbol{-1.00}\ \text{m/s} \)
\( v_{\text{Object 1, Final}} = \boldsymbol{-1.00}\ \text{m/s} \)
\( v_{\text{Object 2, Final}} = \boldsymbol{1.00}\ \text{m/s} \)