To find the momentum of Object 1 before the collision, you need to multiply the mass and the velocity of Object 1.
Reading from the table:
- The mass of Object 1 ([tex]\(m_1\)[/tex]) is 2.0 kg.
- The velocity of Object 1 ([tex]\(v_1\)[/tex]) is 4.0 m/s.
So, the momentum of Object 1 ([tex]\(p_1\)[/tex]) is calculated as follows:
[tex]\[ p_1 = m_1 \times v_1 = 2.0 \, \text{kg} \times 4.0 \, \text{m/s} = 8.0 \, \text{kg} \cdot \text{m/s} \][/tex]
Next, to find the momentum of Object 2 before the collision:
- The mass of Object 2 ([tex]\(m_2\)[/tex]) is 6.0 kg.
- The velocity of Object 2 ([tex]\(v_2\)[/tex]) is 0 m/s.
So, the momentum of Object 2 ([tex]\(p_2\)[/tex]) is:
[tex]\[ p_2 = m_2 \times v_2 = 6.0 \, \text{kg} \times 0 \, \text{m/s} = 0 \, \text{kg} \cdot \text{m/s} \][/tex]
After the collision, the combined mass of Object 1 and Object 2 is given as 8.0 kg, and their combined velocity is 1.0 m/s.
To find the total momentum after the collision:
- The combined mass ([tex]\(m_{\text{combined}}\)[/tex]) is 8.0 kg.
- The combined velocity ([tex]\(v_{\text{combined}}\)[/tex]) is 1.0 m/s.
Therefore, the total momentum after the collision ([tex]\(p_{\text{combined}}\)[/tex]) is:
[tex]\[ p_{\text{combined}} = m_{\text{combined}} \times v_{\text{combined}} = 8.0 \, \text{kg} \times 1.0 \, \text{m/s} = 8.0 \, \text{kg} \cdot \text{m/s} \][/tex]
In summary:
- The momentum of Object 1 before the collision is [tex]\(8.0 \, \text{kg} \cdot \text{m/s}\)[/tex].
- The momentum of Object 2 before the collision is [tex]\(0 \, \text{kg} \cdot \text{m/s}\)[/tex].
- The combined mass after the collision has a total momentum of [tex]\(8.0 \, \text{kg} \cdot \text{m/s}\)[/tex].
So filling in the blanks:
To identify the momentum of Object 1, you must multiply __mass__ and __velocity__.
Object 1 had a momentum of __8.0__ kg·m/s before the collision.
Object 2 had a momentum of __0.0__ kg·m/s before the collision.
The combined mass after the collision had a total momentum of __8.0__.
