Chapter 7, Problem 8A

When a cannon is fired, are the forces on the cannonball and on the cannon equal in magnitude? Are the accelerations of the two equal?

To determine

Whether the force on the cannonball and cannon and there acceleration be equal when the cannon is fired.

Answer to Problem 8A

The force on the cannonball and cannon will be equal but there acceleration will be unequal.

Explanation of Solution

Introduction:

As per Newton’s third law of motion, for every force exerted there is an opposite and equal reaction force.

And, according to Newton’s second law of motion, if the net force $F$ is applied to the mass $m$ , then the acceleration produced is given by,

  $a=\frac{F}{m}$

When the cannon is fired, a force is exerted on the cannon ball. Considering Newton’s third law of motion, every force has an equal and opposite reaction force. Thus, the cannonball will also exert the force of same magnitude but in the opposite direction on the cannon. Thus, the force on the cannon and the cannonball are equal in magnitude.

Now, consider the Newton’s second law of motion. It can be seen that the acceleration produced is inversely proportional to the mass of the object. Thus, when the same force is applied to both the cannonball and cannon, the acceleration produced will be different and depend inversely on their masses.

Conclusion:

Hence, the acceleration produced in the cannonball and cannon are different because the force applied on them are equal but their masses are different.