Question

1. a 1200 kg car moves at 50 km/h east hits a 1100 kg car which was at rest. the two cars attach and now have what momentum?

Explanation:

Step1: Recall the law of conservation of momentum

The law of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, i.e., \( p_{\text{initial}} = p_{\text{final}} \).

Step2: Calculate the initial momentum of the first car

The mass of the first car \( m_1 = 1200 \, \text{kg} \) and its velocity \( v_1 = 50 \, \text{km/h} \) (east). The momentum of the first car \( p_1 = m_1v_1 \). The second car is at rest, so its initial momentum \( p_2 = m_2v_2 = 1100 \, \text{kg} \times 0 \, \text{km/h} = 0 \). The total initial momentum \( p_{\text{initial}} = p_1 + p_2 = m_1v_1 + m_2v_2 \).

Substituting the values: \( p_{\text{initial}} = 1200 \, \text{kg} \times 50 \, \text{km/h} + 1100 \, \text{kg} \times 0 \, \text{km/h} = 1200 \times 50 \, \text{kg·km/h} \).

Step3: Calculate the total mass after collision

After the collision, the two cars stick together, so the total mass \( m_{\text{total}} = m_1 + m_2 = 1200 \, \text{kg} + 1100 \, \text{kg} = 2300 \, \text{kg} \).

Step4: Use conservation of momentum to find the final velocity (and then momentum)

Let the final velocity be \( v_{\text{final}} \). Then \( p_{\text{final}} = m_{\text{total}}v_{\text{final}} \). By conservation of momentum, \( m_1v_1 + m_2v_2 = m_{\text{total}}v_{\text{final}} \). We know \( v_2 = 0 \), so \( 1200 \times 50 = 2300 \times v_{\text{final}} \). Solving for \( v_{\text{final}} \), we get \( v_{\text{final}}=\frac{1200\times50}{2300}=\frac{60000}{2300}=\frac{600}{23}\approx26.09 \, \text{km/h} \) (east).

Then the final momentum \( p_{\text{final}} = m_{\text{total}}v_{\text{final}}=(1200 + 1100)\times\frac{600}{23}=2300\times\frac{600}{23}=60000 \, \text{kg·km/h} \) (east).

Alternatively, since momentum is conserved, the final momentum is equal to the initial momentum of the first car (because the second car had zero initial momentum). So \( p_{\text{final}} = m_1v_1 = 1200 \times 50 = 60000 \, \text{kg·km/h} \) (east).

Answer:

The momentum of the two cars after the collision is \( \boldsymbol{60000 \, \text{kg·km/h}} \) (directed east).