Question

A small stationary satellite deep in space exploded into two pieces one piece has a mass of 500kg the other 1500kg. The 1500kg piece moved away with a velocity of 20ms^1 A)What was the velocity of the 500kg part after explosion B)How much energy was generated in the explosion? State any assumptions you make.

Answer 1

The mass of the first part of the satellite is,

`m_1=500\text{ kg}`

The mass of the second part is,

`m_2=1500\text{ kg}`

The speed of the second part is,

`v_2=20\text{ m/s}`

let the speed of the first part be v1.

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__Part (A)__

applying linear momentum conservation principle we get,

`\begin{gathered} (m_1+m_2)*0=m_1v_1+m_2v_2 \\ v_2=-(m_1v_1)/(m_2) \end{gathered}`

Substituting the values we get,

`\begin{gathered} v_2=(1500*20)/(500) \\ =60\text{ m/s} \end{gathered}`

Hence the velocity of the first part after the explosion is 60 m/s.

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__Part (B)__

the energy generated after the explosion is the kinetic energy of the masses.

we consider no mass is lost here, only the kinetic energy of the parts are the total energy after an explosion.

The kinetic energy after the explosion is,

`\begin{gathered} K=(1)/(2)\mleft\lbrace^{}_{}m_1(v_1)^2+m_2(v_2)^2\mright\rbrace_{}_{} \\ =(1)/(2)\mleft\lbrace500*60^2+1500*20^2\mright\rbrace \\ =1.2*10^6\text{J} \end{gathered}`