Question

An 8000 kg car moving at a constant speed of 14m/s strikes a barrier. The two stick together and move for a while at a speed of 5m/s. What is the mass of the barrier?Show Your Solution using latex

Answer 1

ANSWER:

14400 kg

STEP-BY-STEP EXPLANATION:

Given:

Mass car (m1) = 8000 kg

The initial speed of the car (u1) = 14 m/s

The initial speed of the barrier (u2) = 0 m/s

The final speed of the car and barrier (v) = 5 m/s

We do the momentum balance to be able to determine the mass of the barrier just like this

$\begin{gathered} m_1u_1+m_2u_2=(m_1+m_2)v \\ \\ \text{ We replacing} \\ \\ 8000\cdot14+m_2\cdot0=(8000+m_2)\cdot5 \\ \\ 112000=40000+5m_2 \\ \\ 5m_2=112000-40000 \\ \\ m_2=\frac{72000}{5} \\ \\ m_2=14400\text{ kg} \end{gathered}$

Therefore, the mass of the barrier is equal to 14400 kg