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Question

A cruise ship with a mass of $1.00 \times 10^{7}\ \mathrm{kg}$ strikes a pier at a speed of 0.750 m/s. It comes to rest 6.00 m later, damaging the ship, the pier, and the tugboat captain's finances. Calculate the average force exerted on the pier using the concept of impulse.

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Here the mass of the ship

\begin{align*} m = 1.00\times 10^7\,\mathrm{kg} \end{align*}

Speed of the ship at the time of strike with the pier

\begin{align*} v_{\text{i}} = 0.750\,\mathrm{m\,s^{-1}} \end{align*}

The distance covered by the ship before come to rest

\begin{align*} S = 6.00\,\mathrm{m} \end{align*}

Finally the ship comes to rest, so its final speed is

\begin{align*} v_{\text{f}} = 0.0\,\mathrm{m\,s^{-1}} \end{align*}

Now from the kinametics, we get

\begin{align*} v_{\text{f}}^2 = v_{\text{f}}^2 + 2\,a\,S \end{align*}

By solving the above equation for the acceleration (a), we get

\begin{align*} a & = \frac{v_{\text{f}}^2 - v_{\text{i}}^2}{2\,S}\\ & = \frac{\left(0.0\,\mathrm{m\,s^{-1}} \right)^2 - \left(0.750\,\mathrm{m\,s^{-1}} \right)^2}{2\,\times 6.00\,\mathrm{m}}\\ & = 0.047\,\mathrm{m\,s^{-2}} \end{align*}

Now we know the force is given by

\begin{align*} F & = m\,a\\ & = 1.00\times 10^7\,\mathrm{kg} \times 0.047\,\mathrm{m\,s^{-2}}\\ & = 468750\,\mathrm{N}\\ & = 469\,\mathrm{kN} \end{align*}

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Related questions with answers

A cruise ship with a mass of $1.00 \times 10^{7}\ \mathrm{kg}$ strikes a pier at a speed of 0.750 m/s. It comes to rest 6.00 m later, damaging the ship, the pier, and the tugboat captain's finances. Calculate the average force exerted on the pier using the concept of impulse.

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A cruise ship with a mass of 1.00×107 kg1.00 \times 10^{7}\ \mathrm{kg}1.00×107 kg strikes a pier at a speed of 0.750 m/s. It comes to rest 6.00 m later, damaging the ship, the pier, and the tugboat captain's finances. Calculate the average force exerted on the pier using the concept of impulse.

Create an account to view solutions

Create an account to view solutions

Recommended textbook solutions

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A cruise ship with a mass of $1.00 \times 10^{7}\ \mathrm{kg}$ strikes a pier at a speed of 0.750 m/s. It comes to rest 6.00 m later, damaging the ship, the pier, and the tugboat captain's finances. Calculate the average force exerted on the pier using the concept of impulse.