# A ball with a mass of #8 kg# moving at #7 m/s# hits a still ball with a mass of #16 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?

To find the velocity of the second ball after collision, we use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

(m_1 \times v_1 + m_2 \times v_2 = m_1 \times u_1 + m_2 \times u_2)

(8 \times 7 + 16 \times 0 = 8 \times 0 + 16 \times v_2)

(56 = 16 \times v_2)

(v_2 = \frac{56}{16} = 3.5 , \text{m/s})

To find the kinetic energy lost as heat in the collision, we first calculate the initial kinetic energy and the final kinetic energy:

Initial kinetic energy = ( \frac{1}{2} \times m_1 \times u_1^2 + \frac{1}{2} \times m_2 \times u_2^2 )

Final kinetic energy = ( \frac{1}{2} \times m_1 \times 0^2 + \frac{1}{2} \times m_2 \times v_2^2 )

Kinetic energy lost as heat = Initial kinetic energy - Final kinetic energy

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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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- Is the total momentum always conserved between any two objects involved in a collision?
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- A ball with a mass of #12 kg# moving at #7 m/s# hits a still ball with a mass of #24 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?

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