Question

In a closed system, an object with a mass of 1.5 kg
collides with a second object. The two objects then move together at a velocity of 50 m/s
. The total momentum of the system is 250 kg⋅m/s
. What is the mass of the second object? (1 point)
Responses

1.5 kg
1.5 kg

5.0 kg
5.0 kg

3.5 kg
3.5 kg

3.0 kg

Answer 1

To solve for the mass of the second object in a closed system during a collision, we can use the principle of conservation of momentum.

Given:

- Mass of the first object (m1) = 1.5 kg
- Final velocity of both objects after the collision (v) = 50 m/s
- Total momentum of the system (P_total) = 250 kg⋅m/s

The formula for momentum is:

\[ P = m \times v \]

The total momentum after the collision can be expressed as:

\[ P_{\text{total}} = (m_1 + m_2) \times v \]

Where \( m_2 \) is the mass of the second object. Thus, we can write:

\[ 250 \, \text{kg⋅m/s} = (1.5 \, \text{kg} + m_2) \times 50 \, \text{m/s} \]

Now, we can simplify and solve for \( m_2 \):

1. Divide both sides by 50 m/s:

\[ \frac{250 \, \text{kg⋅m/s}}{50 \, \text{m/s}} = 1.5 \, \text{kg} + m_2 \]

\[ 5 \, \text{kg} = 1.5 \, \text{kg} + m_2 \]

2. Subtract 1.5 kg from both sides:

\[ m_2 = 5 \, \text{kg} - 1.5 \, \text{kg} \]

\[ m_2 = 3.5 \, \text{kg} \]

Therefore, the mass of the second object is **3.5 kg**.

Correct response: **3.5 kg**.