Question

an experiment involves two carts crashing into each other, the results are shown in the diagrams below:

before

• a blue cart of mass \\(4\text{ kg}\\) moving to the right at \\(3\text{ m/s}\\).
• a yellow cart of mass \\(2\text{ kg}\\) at rest.

after

• the blue cart of mass \\(4\text{ kg}\\) moving to the right at \\(1\text{ m/s}\\).
• the yellow cart of mass \\(2\text{ kg}\\) moving to the right at \\(4\text{ m/s}\\).

based on what is observed, which of the following statements could be valid claims (there are multiple correct answers)?

the total momentum after the carts collided is equal to the total momentum before they collided.
the two carts experienced a change in momentum of equal magnitude.
the total momentum has increased after the collision.
the yellow cart gained more momentum than the blue cart lost.

Explanation:

Step1: Calculate initial momentum

$$p_{\text{initial}} = (4\text{ kg} \times 3\text{ m/s}) + (2\text{ kg} \times 0\text{ m/s}) = 12\text{ kg}\cdot\text{m/s}$$

Step2: Calculate final momentum

$$p_{\text{final}} = (4\text{ kg} \times 1\text{ m/s}) + (2\text{ kg} \times 4\text{ m/s}) = 12\text{ kg}\cdot\text{m/s}$$

Step3: Compare total momentum

$$p_{\text{initial}} = p_{\text{final}} = 12\text{ kg}\cdot\text{m/s}$$

Step4: Calculate momentum changes

$$\Delta p_{\text{blue}} = 4 - 12 = -8\text{ kg}\cdot\text{m/s},\quad \Delta p_{\text{yellow}} = 8 - 0 = 8\text{ kg}\cdot\text{m/s}$$

Answer:

• The total momentum after the carts collided is equal to the total momentum before they collided.
• The two carts experienced a change in momentum of equal magnitude.