# A ball with a mass of #4 kg# moving at #6 m/s# hits a still ball with a mass of #10 kg#. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

This is a conservation of momentum problem; find the speed of the second by computing the system momentum before and after:

Replace and solve it; I'll let you see it through to the end.

Is the loss of energy

Wishing you luck, Yonas

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To find the velocity of the second ball after the collision, we can use the principle of conservation of momentum:

[ m_1 \cdot v_1 + m_2 \cdot v_2 = m_1 \cdot u_1 + m_2 \cdot u_2 ]

Where:

- ( m_1 ) = mass of the first ball (4 kg)
- ( m_2 ) = mass of the second ball (10 kg)
- ( v_1 ) = final velocity of the first ball (0 m/s, as it stops moving)
- ( v_2 ) = final velocity of the second ball (unknown)
- ( u_1 ) = initial velocity of the first ball (6 m/s)
- ( u_2 ) = initial velocity of the second ball (0 m/s, as it is still)

Once we find the final velocity of the second ball, we can calculate the kinetic energy lost as heat using the principle of conservation of energy:

[ \text{Kinetic energy lost} = \frac{1}{2} m_1 (u_1^2 - v_1^2) ]

Where:

- ( m_1 ) = mass of the first ball (4 kg)
- ( u_1 ) = initial velocity of the first ball (6 m/s)
- ( v_1 ) = final velocity of the first ball (0 m/s)

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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