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A cruise ship with a mass of 1.03 ✕ 107 kg strikes a pier at a speed of 0.652 m/s. It comes to rest after traveling 4.44 m, damaging the ship, the pier, and the tugboat captain's finances. Calculate the average force (in N) exerted on the pier using the concept of impulse. (Hint: First calculate the time it took to bring the ship to rest, assuming a constant force. Indicate the direction with the sign of your answer.)

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Answer:

The average force exerted on the pier is [tex]4.9 \times 10^{5}[/tex] N

Explanation:

Given :

Mass of ship [tex]m = 1.03 \times 10^{7}[/tex] Kg

Distance [tex]x = 4.44[/tex] m

Velocity [tex]v = 0.652[/tex] [tex]\frac{m}{s}[/tex]

Now find the average velocity,

 [tex]v _{avg} = \frac{0+0.652}{2}[/tex]

 [tex]v _{avg} = 0.326[/tex] [tex]\frac{m}{s}[/tex]

Now find the time taken by ship to travel 4.44 m.

   [tex]t = \frac{x}{v_{avg} }[/tex]

   [tex]t = \frac{4.44}{0.326}[/tex]

   [tex]t = 13.62[/tex] sec

Now calculating average force,

  [tex]F = \frac{m \Delta v}{\Delta t}[/tex]

Where [tex]\Delta v = 0.652 -0[/tex] = 0.652 [tex]\frac{m}{s}[/tex]

  [tex]F = \frac{1.03 \times 10^{7} \times 0.652 }{13.62}[/tex]

  [tex]F = 4.9 \times 10^{5}[/tex] N

Therefore, the average force exerted on the pier is [tex]4.9 \times 10^{5}[/tex] N

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