A block(1) of mass, m1= 3.2 kg, moving at speed 0.85 m/s hits another block (2) m2=2.7 kg at rest. After collision, both blocks stick and slide together on frictionless surface at the same speed. how to find the ratio of Kinetic energy (final/initial) ?
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The ratio of kinetic energy (final/initial) can be found by calculating the initial kinetic energy of block 1, then using the conservation of momentum to find the final velocity of the combined blocks, and finally calculating the final kinetic energy of the combined blocks.

Calculate the initial kinetic energy of block 1 using the formula: ( KE_{initial} = \frac{1}{2} m_1 v_1^2 )

Use the conservation of momentum to find the final velocity of the combined blocks: ( m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f ) Solve for ( v_f ), the final velocity of the combined blocks.

Calculate the final kinetic energy of the combined blocks using the formula: ( KE_{final} = \frac{1}{2} (m_1 + m_2) v_f^2 )

Finally, find the ratio of kinetic energy (final/initial): ( \text{Ratio} = \frac{KE_{final}}{KE_{initial}} )
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When evaluating a onesided 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 onesided 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 onesided 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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