Question

The largest grand piano in the world is really grand. Built in London, it has a mass of 1,152 kg. Suppose a pianist finishes playing this piano and pushes herself from the piano so that she rolls backwards with a speed of 1.5 m/s. Meanwhile, the piano rolls forward with a constant velocity of 0.06 m/s. Assuming the stool that the pianist is sitting on has a negligible mass, what is the pianist’s mass? Round to the hundredths.

Answer 1

46.08 kg

Explanation:

Given

m1 = 1152 kg

v1 = 0.06 m/s

v2 = -1.5 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 plug in and calculate for the mass, just like this:

`\begin{gathered} 0_{}=m_1\cdot V_1+m_2\cdot V_2 \\ 0=1152\cdot0.06+m_2\cdot-1.5 \\ -1.5m_2=-69.12 \\ m_2=(-69.12)/(-1.5) \\ m_2=46.08\text{ kg} \end{gathered}`

Which means that the mass of the pianist is 46.08 kg