In a closed system, an object with a mass of 10 kg moves at a velocity of 5.4 m/s. It collides with a second object that has a mass of 12 kg and that is moving in the opposite direction with a velocity of 3.5 m/s. What is the total momentum of the system after the collision?(1 point)

Question

Responses

54 kg-m/s
54 kg-m/s

12 kg-m/s
12 kg-m/s

66 kg-m/s
66 kg-m/s

42 kg-m/s

Answer 1

To calculate the total momentum of the system after the collision, we first need to find the initial momentum of both objects before the collision.

1. Calculate the momentum of the first object (mass = 10 kg, velocity = 5.4 m/s): \[ p_1 = m_1 \times v_1 = 10 , \text{kg} \times 5.4 , \text{m/s} = 54 , \text{kg-m/s} \]

2. Calculate the momentum of the second object (mass = 12 kg, velocity = -3.5 m/s; the negative sign indicates it is moving in the opposite direction): \[ p_2 = m_2 \times v_2 = 12 , \text{kg} \times (-3.5 , \text{m/s}) = -42 , \text{kg-m/s} \]

3. Find the total initial momentum of the system: \[ p_{\text{total}} = p_1 + p_2 = 54 , \text{kg-m/s} + (-42 , \text{kg-m/s}) = 54 , \text{kg-m/s} - 42 , \text{kg-m/s} = 12 , \text{kg-m/s} \]

In a closed system, momentum is conserved, so the total momentum after the collision is the same as the total momentum before the collision.

Thus, the total momentum of the system after the collision is:

12 kg-m/s