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

3.0 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.

The total momentum of a closed system before and after the collision remains the same. The momentum before the collision can be expressed as the sum of the momenta of both objects.

Given:
- Mass of the first object (m1) = 1.5 kg
- Final velocity of both objects after collision (v) = 50 m/s
- Total momentum (P) = 250 kg·m/s

First, we calculate the total momentum after the collision:

\[
P = (m_1 + m_2) \cdot v
\]

Where:
- m2 = mass of the second object
- v = final velocity = 50 m/s

Setting the total momentum equal to P:

\[
250 \text{ kg·m/s} = (1.5 \text{ kg} + m_2) \cdot 50 \text{ m/s}
\]

Now, we can 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. Solve for \( m_2 \):

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

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

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