- #1

mister_okay

- 20

- 0

PROPORTION...for example, 5 times the mass of the gun and 5 times

the mass of the bullet...would the recoil experienced by the shooter

be the same as the recoil experienced by the same shooter where the

masses were not increased? For example:

A normal sized gun of 20 kg, and a bullet of 2 kg (these were made

up by myself and are not actual measurements). Increase the masses

by 5, giving us a gun of 100 kg and a bullet of 10 kg. Would the

recoil experienced by the same person be exactly the same in both

cases?

Here is how I initially reasoned it:

F = ma. Assuming that an acceleration of 100 m/s² is required for

the bullet of 2 kg, the force that the bullet feels is 200 N (F =

(2kg)(100m/s²)). The equal and opposite force on the gun would be -

200 N (because every action has an equal and opposite reaction).

Therefore, the acceleration felt by the gun would be -10 m/s² (-200

N = (20kg)(acceleration)).

Increasing the masses proportionally, we now have a gun of 100 kg

and a bullet of 10 kg. If the masses increase, the force required

in order to produce the same acceleration for the bullet would also

have to increase. Therefore, 5F = 5ma...F = 1000 N. The

acceleration of the bullet will still be 100 m/s². The force that

the gun experiences will be equal and opposite: -1000 N. Therefore,

the acceleration the gun experiences will be -10 m/s² (-1000N =

100kg)(acceleration)). In both the 20 kg and the 100 kg gun, the

recoil accelerations are -10 m/s².

From these calculations I deduced that the recoil experienced by the

same shooter must be the same. However, I would like to verify if

this is correct.