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 3,467 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 2.40 m/s to the right. The cart begins to roll to the left at a speed of 0.02 m/s. Assuming the cart’s mass is negligible, what is the librarian’s mass? Round to the hundredths.

Answer 1

Given data

*The given complete set has a mass is m = 3467 kg

*The speed of the cart with a horizontal velocity relative to the floor is v_1 = 0.02 m/s

*The speed of the librarian is v_2 = 2.40 m/s

The formula for the librarian's mass (m_l) is given by the conservation of momentum as

$mv_1=m_lv_2$

Substitute the known values in the above expression as

$\begin{gathered} 3467\times0.02=m_l\times2.40 \\ m_l=\frac{3467\times0.02}{2.40} \\ =28.89\text{ kg} \end{gathered}$

Hence, the librarian's mass is m_l = 28.89 kg