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 \( m_2 \):
- Divide both sides by 50 m/s:
\[ \frac{250 , \text{kg⋅m/s}}{50 , \text{m/s}} = 1.5 , \text{kg} + m_2 \]
\[ 5 , \text{kg} = 1.5 , \text{kg} + m_2 \]
- 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.
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