Question

A spring ball of mass 0.5kg is dropped fro some height .on falling freely for 10s it explodes into two fragments of mass ratio 1:2. The lighter fragment continues to travel downwards with speed of 60m/s .Calculate kinetic energy supplied during explosion

Answer 1

Answer:

Kinetic energy supplied during explosion is 200 J

Explanation:

After the spring mass system is released from rest the system will fall down under gravity

So after t = 10 s the speed of the spring mass system is given as

$v = v_i + at$

$v = 0 + 10(10)$

$v = 100 m/s$

Now we know by momentum conservation

$Mv_1 = m_1v_{1f} + m_2v_{2f}$

here we have

$M(100) = \frac{M}{3}(60) + \frac{2M}{3}v_{2f}$

$100 = 20 + \frac{2}{3}v_{2f}$

$v_{2f} = 120 m/s$

now kinetic energy supplied by the explosion is given as

$\Delta KE = \frac{1}{2}(\frac{0.5}{3})(60^2) + \frac{1}{2}(\frac{1}{3})(120)^2 - \frac{1}{2}(0.5)(100)^2$

$\Delta KE = 200 J$

#Learn

Topic : Momentum conservation

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