Question

Being sold at an army surplus store is a pen gun. The pen gun fires a .22 caliber cartridge with a short barrel that has no rifling, so it must be shot at very close range such as 2ft or 3ft to do damage. What is the pen gun’s diameter in inches?

Answer 1

Using the given information, the recoil velocity of a 1.00-kg plunger and the average force exerted upon it by the gun when a 0.0200-kg bullet is fired at 600 m/s can be calculated. A comparison of forces can also be made between stopping the plunger over a distance of 20.0 cm and accelerating the bullet to its velocity in 10 ms.

Step-by-step explanation:

The question relates to the concept of conservation of momentum and its implications in terms of recoil velocity and forces in firearms. We can calculate the recoil velocity using conservation of momentum. The pen gun's diameter is irrelevant to the physics calculations provided; however, since the gun fires a .22 caliber cartridge, the diameter in inches is .22 inches.

Calculations

Recoil velocity of the plunger: Using conservation of momentum we have the momentum before firing (at rest) is 0 = momentum after firing, i.e., (mass of bullet × velocity of bullet) = (mass of plunger × recoil velocity of plunger). From this, we calculate the recoil velocity.

Average force exerted on the plunger: Using the work-energy theorem, average force × stopping distance = change in kinetic energy of the plunger. We can find the average force from this relationship.

Force comparison: We compare the force on the gun exerted over the stopping distance of 20 cm to the force if the bullet is accelerated to its velocity in 10 ms to see how the force differs in these scenarios.