Object 1 has a velocity of 3 m/s and a mass of 5 kg. Object 2 also has a mass of 5 kg but isn't moving. Object 1 collides with Object 2 and they move off together. Work out their velocity using the principle of conservation of momentum.
Question
Object 1 has a velocity of 3 m/s and a mass of 5 kg. Object 2 also has a mass of 5 kg but isn't moving. Object 1 collides with Object 2 and they move off together. Work out their velocity using the principle of conservation of momentum.
Solution
The principle of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, provided no external forces are acting.
Step 1: Calculate the initial momentum The initial momentum is the momentum of Object 1 because Object 2 isn't moving. Momentum is calculated as mass times velocity. So, for Object 1, the momentum is 5 kg * 3 m/s = 15 kg*m/s.
Step 2: Calculate the final momentum After the collision, the two objects move together. The total mass is now 5 kg (Object 1) + 5 kg (Object 2) = 10 kg. We don't know the final velocity yet, let's call it v. So the final momentum is 10 kg * v.
Step 3: Set the initial momentum equal to the final momentum According to the principle of conservation of momentum, the initial and final momentum are equal. So, we set them equal to each other and solve for v:
15 kgm/s = 10 kg * v v = 15 kgm/s / 10 kg = 1.5 m/s
So, the velocity of the two objects moving together after the collision is 1.5 m/s.
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