Question

In a closed system, an object with a mass of 1.5 kg
1.5

kg
collides with a second object. The two objects then move together at a velocity of 50 m/s
50

m/s
. The total momentum of the system is 250 kg⋅m/s
250

kg
⋅
m/s
. What is the mass of the second object? (1 point)
Responses

3.0 kg
3.0 kg

1.5 kg
1.5 kg

3.5 kg
3.5 kg

5.0 kg

Answer 1

To find the mass of the second object, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

Given:
- Mass of the first object \( m_1 = 1.5 \, \text{kg} \)
- Final velocity of both objects \( v_f = 50 \, \text{m/s} \)
- Total momentum of the system \( p_{\text{total}} = 250 \, \text{kg} \cdot \text{m/s} \)

The momentum after the collision (when both objects move together) can be expressed as:
\[
p_{\text{total}} = (m_1 + m_2) \cdot v_f
\]
Where \( m_2 \) is the mass of the second object.

Substituting the values we have:
\[
250 \, \text{kg} \cdot \text{m/s} = (1.5 \, \text{kg} + m_2) \cdot 50 \, \text{m/s}
\]

Now, let's solve for \( m_2 \):
\[
250 = (1.5 + m_2) \cdot 50
\]

Dividing both sides by 50:
\[
5 = 1.5 + m_2
\]

Subtracting 1.5 from both sides gives:
\[
m_2 = 5 - 1.5 = 3.5 \, \text{kg}
\]

Therefore, the mass of the second object is \( \boxed{3.5 \, \text{kg}} \).