Two objects, one with a mass of 2 kg and the other with a mass of 3 kg, collide in two dimensions resulting in an inelastic collision. Calculate the final velocity of the combined system.
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To solve this problem, we can use the principle of conservation of momentum. In an inelastic collision, the two objects stick together after collision, so we can treat them as a single system with a combined mass.
Let the initial velocities of the two objects be v1 and v2, and let the final velocity of the combined system be vf.
The momentum before the collision is given by:
Initial momentum = m1 * v1 + m2 * v2
where m1 and m2 are the masses of the two objects.
The momentum after the collision is given by:
Final momentum = (m1 + m2) * vf
According to the conservation of momentum, the initial momentum should equal the final momentum. Therefore, we have the equation:
m1 * v1 + m2 * v2 = (m1 + m2) * vf
Plugging in the given values, we have:
(2 kg) * v1 + (3 kg) * v2 = (2 kg + 3 kg) * vf
2v1 + 3v2 = 5vf
We also know that the combined mass of the system is (2 kg + 3 kg) = 5 kg.
Let's assume v1 = 1 m/s and v2 = 2 m/s for the initial velocities of the two objects. Plugging these values into the equation, we have:
2(1) + 3(2) = 5vf
2 + 6 = 5vf
8 = 5vf
Now, we can solve for vf:
vf = 8 / 5
vf = 1.6 m/s
Therefore, the final velocity of the combined system is 1.6 m/s.
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