Answer to Question #110754 in Mechanics | Relativity for Bianca

Question

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))

Answer 1

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,

$m_1v_1+m_2v_2+m_3v_3=MV$

Now, substituting the values,

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

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

$\Rightarrow v_3=-62.63 m/sec$