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प्रश्न
The mass of a cyclist together with the bike is 90 kg. Calculate the increase in kinetic energy if the speed increases from 6⋅0 km/h to 12 km/h.
योग
उत्तर
Total mass of the system (cyclist and bike), \[M = m_c + m_b = 90 kg\]
Initial velocity of the system, \[u = 6 . 0 \text{ km } /h = 1 . 666 \text{ m } /\sec\]
Final velocity of the system, \[\nu = 12 \text{ km } /h = 3 . 333 \text{ m }/\sec\]
From work-energy theorem, we have:
\[\text{ Increase in K . E }. = \frac{1}{2}M \nu^2 - \frac{1}{2}m u^2 \]
\[ = \frac{1}{2}90 \times \left( 3 . 333 \right)^2 - \frac{1}{2} \times 90 \times \left( 1 . 66 \right)^2 \]
\[ = 499 . 4 - 124 . 6\]
\[ = 374 . 8 = 375 J\]
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