In an elastic collision involving two objects of equal mass, both momentum and kinetic energy are conserved. Given this, we can make some predictions about the outcome of the collision.
Hypothesis:
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Initial Momentum:
- Let’s denote the two objects as Object A and Object B, both having the same mass (m). If Object A is moving with an initial velocity \( v_A \) while Object B is initially at rest (\( v_B = 0 \)), the initial momentum of the system can be expressed as: \[ P_{initial} = m \cdot v_A + m \cdot 0 = m \cdot v_A \]
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Final Velocity Prediction:
- In a perfectly elastic collision with equal masses, it is often found that the two objects will exchange their velocities. Therefore, after the collision, we predict that:
- Object A will come to rest (\( v'_A = 0 \)).
- Object B will move with the initial velocity of Object A (\( v'_B = v_A \)).
- In a perfectly elastic collision with equal masses, it is often found that the two objects will exchange their velocities. Therefore, after the collision, we predict that:
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Final Momentum:
- The final momentum of the system can thus be expressed as: \[ P_{final} = m \cdot 0 + m \cdot v_A = m \cdot v_A \]
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Conservation of Kinetic Energy:
- The initial kinetic energy of the system can be calculated as: \[ KE_{initial} = \frac{1}{2} m v_A^2 \]
- After the collision, the kinetic energy will also account for Object B's velocity: \[ KE_{final} = \frac{1}{2} m \cdot 0^2 + \frac{1}{2} m v_A^2 = \frac{1}{2} m v_A^2 \]
- Thus, the total kinetic energy remains the same, confirming the conservation of kinetic energy.
Conclusion:
Based on these predictions, we hypothesize that during a 100% elastic collision between two objects of equal mass, one initially at rest and the other in motion, the moving object will stop, and the stationary object will move away with the same speed as the initially moving object. This illustrates the principles of momentum and kinetic energy conservation in elastic collisions.
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