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Chapter 11: Q. 66 (page 290)

Old naval ships fired 10 kg cannon balls from a 200 kg cannon. It was very important to stop the recoil of the cannon, since otherwise the heavy cannon would go careening across the deck of the ship. In one design, a large spring with spring constant 20,000 N/m was placed behind the cannon. The other end of the spring braced against a post that was firmly anchored to the ship’s frame. What was the speed of the cannon ball if the spring compressed 50 cm when the cannon was fired?

Short Answer

Expert verified

Speed of the cannon ball is 100 m/s.

Step by step solution

01

Step 1. Given information is :Mass of cannon M = 200 kgMass of the cannon ball m = 10 kgSpring constant k = 2000 N/mDistance by which spring is compressed∆x=50 cm=0.5m

We need to find out the speed of the cannon ball if the spring if the compressed by 50 cm when the cannon was fired

02

Step 2. Using the Law of conservation of momentum and Law of conservation of Energy

Let velocity of cannon = V

Velocity of cannon ball = v

Using Law of conservation of Momentum,

MV=mvv=MmV

Using Law of conservation of Energy,

12k(∆x)2=12MV220000(0.5)2=200V2V2=25V=5m/sAndweknowthat,v=MmVv=20010×5=100m/s

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