Chapter 8, Problem 15A

In terms of momentum conservation, why does a cannon recoil when fired?

To determine

The reason that a cannon recoil when fired in terms of momentum conservation.

Answer to Problem 15A

Since initial net momentum is zero, thus to make the final momentum zero, the cannon recoil in opposite direction of the motion of cannonball.

Explanation of Solution

Introduction:

Momentum is given by the product of the mass $\left(m\right)$ of the object and its velocity $\left(v\right)$ as,

  $p=mv$

And, law of conservation of momentum is given by,

  ${\left(\text{net momentum}\right)}_{\text{initial}}={\left(\text{net momentum}\right)}_{\text{final}}$

Since initially both the cannon and cannonball are at rest, thus the initial momentum of the system is zero. Thus,

  $0=p_{\text{cannon}}+p_{\text{cannonball}}$

Or,

  $m_{\text{cannon}}{v}_{\text{cannon}}=-\left(m_{\text{cannonball}}{v}_{\text{cannonball}}\right)$

Conclusion:

When fired, the cannon moves in opposite direction of motion of the cannonball, and hence it recoils.