To find the mass of the second object, we can use the principle of conservation of momentum. The total momentum before the collision must equal the total momentum after the collision.
Given:
- Mass of the first object \( m_1 = 1.5 , \text{kg} \)
- Velocity after collision \( v_f = 50 , \text{m/s} \)
- Total momentum \( P = 250 , \text{kg⋅m/s} \)
The total momentum after the collision (when both objects are moving together) can be expressed as: \[ P = (m_1 + m_2) \cdot v_f \]
Substituting the known values: \[ 250 , \text{kg⋅m/s} = (1.5 , \text{kg} + m_2) \cdot 50 , \text{m/s} \]
Now, solving for \( m_2 \): \[ 250 = (1.5 + m_2) \cdot 50 \] \[ 250 = 75 + 50m_2 \] \[ 250 - 75 = 50m_2 \] \[ 175 = 50m_2 \] \[ m_2 = \frac{175}{50} = 3.5 , \text{kg} \]
Therefore, the mass of the second object is 3.5 kg.
1 answer