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The largest single publication in the world is the 1112-volume set of British Parliamentary Papers for 1968 through 1972. The complete set has a mass of 3.3 × 10^3 kg. Suppose the entire publication is placed on a cart that can move without friction. The cart is at rest, and a librarian is sitting on top of it, just having loaded the last volume. The librarian jumps off the cart with a horizontal velocity relative to the floor of 2.5 m/s to the right. The cart begins to roll to the left at a speed of 0.05 m/s. Assuming the cart’s mass is negligible,what is the librarian’s mass?

Respuesta :

Answer:

[tex]m_l=550\ kg[/tex] is the mass of librarian.

Explanation:

Given:

  • mass of the system, [tex]m_s=3.3\times 10^{3}\ kg[/tex]
  • velocity of librarian relative to the ground, [tex]v_l=2.5\ m.s^{-1}[/tex]
  • velocity of the cart relative to the ground, [tex]v_c=0.5\ m.s^{-1}[/tex]

Now using the principle of elastic collision:

Net momentum of the system is zero.

[tex]m_l\times v_l=(3300-m_l)\times v_c[/tex]

[tex]m_l\times 2.5=(3300-m_l)\times 0.5[/tex]

[tex]m_l=550\ kg[/tex] is the mass of librarian.

Answer:

660 kg

Explanation:

Using conservation of momentum:

[tex]P_{f} =P_{i}[/tex]

The initial momentum of cart + librarian is zero because at rest!

[tex]P_{i} = 0\\P_{f} = 0[/tex]

The final momentum can be calculated as follows:

[tex]P_{f} = m_{publication}*v_{cart} + m_{librarian}*v_{librarian} \\\\m_{librarian} = \frac{- m_{publication}*v_{cart}}{v_{librarian}} \\\\m_{librarian} = \frac{- 3.3*10^3*0.05}{-2.5} \\\\m_{librarian} = 660kg[/tex]

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