Object A with mass 6.7 kg is moving at 5.1 m/s. Object B with mass 7.4 kg is moving at 4.7 m/s. Object B impacts Object A, and they stick together. With what velocity do the objects move?
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To find the velocity at which the objects move together after the impact, we can use the principle of conservation of momentum. According to this principle, the total momentum before the impact should be equal to the total momentum after the impact.
The momentum of an object can be calculated by multiplying its mass with its velocity. Mathematically, momentum (p) can be calculated as:
p = mass × velocity
Before the impact, the momentum of Object A (pA) can be calculated as:
pA = mass of A × velocity of A
= 6.7 kg × 5.1 m/s
= 34.17 kg·m/s
Similarly, the momentum of Object B (pB) can be calculated as:
pB = mass of B × velocity of B
= 7.4 kg × 4.7 m/s
= 34.78 kg·m/s
Since the objects stick together after the impact, the total momentum after the impact (pAB) will be the sum of the individual momenta:
pAB = pA + pB
= 34.17 kg·m/s + 34.78 kg·m/s
= 68.95 kg·m/s
To find the final velocity (v) at which the objects move together, we need to divide the total momentum by the combined mass of the objects.
Combined mass (mAB) = mass of A + mass of B
= 6.7 kg + 7.4 kg
= 14.1 kg
v = pAB / mAB
= 68.95 kg·m/s / 14.1 kg
≈ 4.89 m/s
Therefore, after the impact, Object A and Object B will move together with a velocity of approximately 4.89 m/s.