# Find the Ratio of Recoil Velocities: Blank vs Standard Cartridge

• cstout
In summary, the problem involves an individual standing on a slippery surface firing a gun with a standard cartridge and a blank cartridge. The ratio of the recoil speeds is to be found using conservation of momentum. The initial momentum is zero and the momentum after firing can be used to calculate the recoil speeds.
cstout

## Homework Statement

A person is standing on a sheet of ice so slippery that friction may be ignored. This individual fires a gun parallel to the ground. When a standard cartridge is used , a 14-g bullet is shot forward with a speed of 270 m/s, and the person recoils with a speed of vc. When a blank cartridge is used , a mass of 0.13g is shot forward with a speed of 53 m/s , and the recoil speed is vb. Find the ratio vb/vc.

vb/vc

## The Attempt at a Solution

i simply tried mass(velocity) for each one and did vb/vc to get .0018 but the answer is not right. I'm not sure if i have an error or if those are the wrong steps

Use conservation of momentum. P=mv.

for the first part P = 3.78 kgm/s (converting 14g to kg) and the second part is P = .00689 kgm/s(also converting .13g to kg) and I divided (.00689/3.78) to get .0018 again. Or is there a step in between that I am missing

All you're doing is dividing the momentums of the bullets after being fired by each other.

Instead you need to use conservation of momentum to find the recoil speeds in each case. A problem is that the gun's mass is unknown, but when you take the ratios of the two speeds the mass will cancel

what would you use to find the recoil speeds then?

Conservation of momentum

initially the momentum before firing is 0. Then you fire and the bullet is going one way with such and such momentum, and the gun is going the other way, so you can find the necessary momentum so that the total is still 0 like it was initially

## 1. What is the purpose of finding the ratio of recoil velocities?

The purpose of finding the ratio of recoil velocities is to determine the difference in the velocities of a blank cartridge and a standard cartridge when fired from the same firearm. This can provide insight into the potential effects of using a blank cartridge in place of a standard cartridge.

## 2. How is the ratio of recoil velocities calculated?

The ratio of recoil velocities is calculated by dividing the recoil velocity of the blank cartridge by the recoil velocity of the standard cartridge. This can be done by measuring the velocities using a chronograph or by using the mass and velocity of the projectiles.

## 3. What factors can affect the ratio of recoil velocities?

The ratio of recoil velocities can be affected by various factors such as the weight and type of bullet, the type and amount of gunpowder used, the length and design of the barrel, and the overall weight and design of the firearm.

## 4. Why is it important to consider the ratio of recoil velocities?

Considering the ratio of recoil velocities is important because it can provide information about the performance and safety of using blank cartridges in certain firearms. It can also help in determining the potential impact on the shooter and the firearm itself.

## 5. Can the ratio of recoil velocities be used to compare different types of firearms?

The ratio of recoil velocities can be used to compare different types of firearms only if they are using the same type of ammunition. The ratio will be affected by the specific characteristics of the firearm and the ammunition used, so it cannot be used as a direct comparison between different firearms using different types of ammunition.

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