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An object of mass m1 = 19 kg and velocity v1 = 1.5 m/s crashes into another object of mass m2 = 8 kg and velocity v2 = −13.5 m/s. The two particles stick together as a result of the collision. Because no external forces are acting, the collision does not change the total momentum of the system of two particles, so the principle of conservation of linear momentum applies. m1v1i + m2v2i = (m1 + m2)vf If Jed and Kadia use the one-dimensional conservation of momentum equation to find the final velocity of the two joined objects after the collision, what do they obtain? (Indicate the direction with the sign of your answer.)

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cjrodriguez89

Answer: -2.9 m/s

Explanation:

If we assume that no external forces act during the collision, total momentum must be conserved.

If the collision is completely inelastic, so both masses continue stuck together after it, we can consider that the system behaves like it were a single mass, with a single speed.

So, we can write the following:

p₁ = p₂ ⇒ m₁.v₁ + m₂.v₂ = (m₁ + m₂) vf

Replacing by the values, and solving for vf, we get:

vf = (19 kg. 1.5 m/s + (8 Kg. (-13.5 m/s)) / 19 kg + 8 Kg = -2.9 m/s.

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