To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum of the system before the collision is equal to the total momentum of the system after the collision, assuming no external forces are acting on the system.
Let's denote:
- Mass of body P (m₁) = 8 kg
- Velocity of body P (v₁) = 30 m/s (to the right, we consider this as positive)
- Mass of body Q (m₂) = unknown
- Velocity of body Q (v₂) = -15 m/s (moving in the opposite direction, we consider this as negative)
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Calculate the momentum before the collision: The momentum of body P before collision: \[ p_1 = m_1 \cdot v_1 = 8 , \text{kg} \cdot 30 , \text{m/s} = 240 , \text{kg·m/s} \]
The momentum of body Q before collision: \[ p_2 = m_2 \cdot v_2 = m_2 \cdot (-15 , \text{m/s}) = -15m_2 , \text{kg·m/s} \]
Total momentum before collision: \[ p_{\text{total before}} = p_1 + p_2 = 240 - 15m_2 \]
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We need to consider the velocity of body Q after the collision. Since we don't have information regarding the collision type (elastic or inelastic) or the final velocity, we generally assume body P comes to rest and body Q continues. Let’s just focus on mass calculations first.
For simplicity, if we consider that after the collision, some fraction of their momentum is used up.
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Assuming conservation of momentum: \[ m_1 v_1 + m_2 v_2 = m_1 v_{1f} + m_2 v_{2f} \]
If the result of the collision is not specified, some details about whether the collision is perfectly elastic, inelastic, or whether any of the bodies reverses direction can also affect the result.
For a simple case, let’s assume Q ends up moving in the same direction (which is less likely due to loss of energy). We can only make guesses without strict final conditions:
Given the uncertainty, shall we stick to finding mass based purely on momentum cut with any final velocity? Or would you like to specify the outcome post collision to streamline the calculations?
However, once Q stops or reverses, the direction dictates negative momentum also played.
In short, please specify final velocities, or clarify further condition needed!
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