Answer to Question #110754 in Mechanics | Relativity for Bianca

Question #110754
A 18 g marble shatters into three pieces as shown in the figure above due to thermal stress. Piece one weighs 4.1g & is travelling at a speed of 58m/s-1. Piece 2 weighs 4.7g & is travelling at a speed of 72m/s-1 & piece 3 weighs 9.2g.

What is the speed of the third piece of the marble moving with after the shattering? (in m s−1 to 2 s.f))
Expert's answer

As per the given question,

Total mass of the ball(M) =18g

Initial speed of the larger mass (V)=0

mass of first piece "(m_1)=4.1g"

speed of the first piece "(v_1)=58 m\/sec"

mass of piece 2, "(m_2)=4.7g"

Speed of the piece 2, "(v_2)=72 m\/sec"

mass of piece 3, "(m_3)=9.2g"

Let the speed of the third piece is "(v_3)=?"

Now applying the conservation of momentum,


Now, substituting the values,

"4.1\\times 58+4.7\\times72+9.2\\times v_3=0"

"\\Rightarrow v_3=\\dfrac{-576.2}{9.2} m\/sec"

"\\Rightarrow v_3=-62.63 m\/sec"

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