Don't stand directly behind a cannon

Classical Mechanics Level 2

The cannons on 19th century frigates were ponderous things. For example, on the USS Constitution, a frigate used in the War of 1812, the cannons were \(3~\mbox{meters}\) long, had a mass of \(3000~\mbox{kg}\), and could fire a \(10 ~\mbox{kg}\) cannonball up to a kilometer away. Needless to say the recoil on the cannons was tremendous and a mechanism had to be devised to keep the cannons from careening across the deck. The system employed at the time consisted of rope and tackle, which basically caught the cannon. One wants to make sure that the ropes are strong enough, so one needs to know the magnitude of the forces necessary to stop the cannon. A cannon \(4~\mbox{m}\) above the waterline fires a \(10~\mbox{kg}\) cannonball horizontally that hits the water \(500~\mbox{m}\) away. It recoils and is stopped by a rope braking mechanism, which exerts a constant force on the cannon once it starts to recoil. If the cannon recoils \(1~\mbox{m}\), what is the force the rope braking mechanism exerts on the cannon in Newtons?

Details and assumptions

  • You may neglect air resistance for the motion of the cannonball.
  • The acceleration due to gravity is \(-9.8~\mbox{m/s}^2\).

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