Question

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 3,548 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 2.65 m/s to the right. The cart begins to roll to the left at a speed of 0.03 m/s. Assuming the cart’s mass is negligible, what is the librarian’s mass? Round to the hundredths.

Answer 1

40.17 kg

Explanation:

Given:

m1 = 3548 kg

V1 = -0.03 m/s

V2 = 2.65 m/s

We apply law of conservation of linear momentum:

`\begin{gathered} P_i=P_f \\ P_i=0 \\ P_f=m_1\cdot V_1+m_2\cdot V_2 \end{gathered}`

We replace and calculate the mass as follows:

`\begin{gathered} m_1\cdot V_1+m_2\cdot V_2=0 \\ 3548\cdot-0.03+2.65\cdot m_2=0 \\ -106.44+2.65\cdot m_2=0 \\ m_2=(106.44)/(2.65) \\ m_2=40.17\text{ kg} \end{gathered}`

Therefore the mass is equal to 40.17 kg