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

3.5 kg
3.5 kg

5.0 kg
5.0 kg

1.5 kg
1.5 kg

3.0 kg

Answer 1

To find the mass of the second object, we can use the principle of conservation of momentum. The total momentum before the collision equals the total momentum after the collision.

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

The momentum of the system after the collision can be expressed as:
\[
p_{\text{total}} = (m_1 + m_2) v_f
\]
where \( m_2 \) is the mass of the second object.

Substituting the known values into the equation:
\[
250 = (1.5 + m_2) \cdot 50
\]

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

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

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

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