Question

3 kg ball traveling to the left at a velocity of 2.3 m/s collides with another 0.5 kg ball traveling to the left at 0.3 m/s. As a result of the collision the 3 kg ball moves to the left with a velocity of 1.73 m/s. Using the conservation of momentum calculate the velocity of the 0.5 kg ball after the collision. Show all your work.

Answer 1

Answer on Question #72357-Physics-Other

3 kg ball traveling to the left at a velocity of 2.3 m/s collides with another 0.5 kg ball traveling to the left at 0.3 m/s. As a result of the collision the 3 kg ball moves to the left with a velocity of 1.73 m/s. Using the conservation of momentum calculate the velocity of the 0.5 kg ball after the collision.

Solution

Using the conservation of momentum

$$m _ {1} v _ {1} + m _ {2} v _ {2} = m _ {1} v _ {1} ^ {\prime} + m _ {2} v _ {2} ^ {\prime}$$

The velocity of the 0.5 kg ball after the collision is

$$v _ {2} ^ {\prime} = v _ {2} + \frac {m _ {2}}{m _ {1}} (v _ {1} - v _ {1} ^ {\prime})$$ $$v _ {2} ^ {\prime} = 0.3 + \frac {3}{0.5} (2.3 - 1.73) = 3.72 \frac {m}{s} \text{ to the left}.$$

Answer: $3.72 \frac{m}{s}$ to the left.

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