Answer to Question #83764 in Physics for Carl

Question

A 9.00 kg mass is moving to the right with a velocity of 14.0 m/s. A 12.0kg mass is moving to the left with a velocity of 5.00 m/s. Assuming that these two balls have a head on collision and stick together, what will be the final velocity of the combination?

Answer 1

Answer on Question 83764, Physics, Other

Question:

A 9.0 kg mass is moving to the right with a velocity of 14.0 m/s. A 12.0 kg mass is moving to the left with a velocity of 5.0 m/s. Assuming that these two balls have a head on collision and stick together, what will be the final velocity of the combination?

Solution:

We can find the final velocity of the combination from the law of conservation of momentum:

$$m_1v_1+m_2v_2=(m_1+m_2)v_f,$$

here,

$$m_1=9.0kg$$

is the mass moving to the right,

$$m_2=12.0 kg$$

is the mass moving to the left,

$$v_1=14.0 m/s$$

is the velocity of the mass moving to the right,

$$v_2=5.0 m/s$$

is the velocity of the mass moving to left,

$$v_f$$

is the final velocity of the combination.

Let's choose the direction to the right as the positive. Then, we can write:

$$m_1v_1-m_2v_2=(m_1+m_2)v_f,$$ $$v_f=(m_1v_1-m_2v_2)/(m_1+m_2).$$

Finally, let's substitute the numbers:

$$v_f=(9.0kg * 14.0m/s - 12.0kg * 5.0m/s)/(9.0kg + 12.0 kg)=3.14m/s.$$

Answer:

$$v_f=3.14m/s$$

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