# Gun and Shell: Calculate Velocity and Force

• milan.007
In summary, the conversation discusses a homework problem involving a gun firing a shell and the calculation of the velocity of recoil and the force required to stop the gun. The solution involves using the principle of conservation of momentum and calculating the time taken using initial and final velocities and distance. The discrepancy in the final answer is due to assuming a constant velocity rather than finding the correct value of time.
milan.007

## Homework Statement

A gun of mass 500Kg fires a shell of mass 2Kg with a muzzle velocity of 500m/s.
Calculate:
i) the velocity of recoil of the gun
ii) the force required to stop the gun in a distance of 0.25m

## The Attempt at a Solution

i)I got the velocity of the gun by using the principal of conservation of momentum:
(500)(0) + (2)(0) = 500v + (500)(2). I got 2m/s.

ii)First i used v=d/t, 2=0.25/t, I got 0.125 seconds.
Then i used Force = change in momentum/time taken.
I get 8000N but the book says 4000N.
Im not sure what I am doing wrong??

milan.007 said:
First i used v=d/t …

Hi milan!

You've assumed the velocity is constant (at 2 m/sec).

That gave you the wrong value of t.

Can you see some other way to calculate t (from initial velocity, final velocity, and distance)?

I would like to point out that the calculation for the velocity of the gun in the first part is correct. However, in the second part, the calculation for the force required to stop the gun is incorrect.

The correct approach would be to use the equation F=ma, where F is the force, m is the mass of the gun, and a is the acceleration. We can calculate the acceleration using the equation v^2=u^2+2as, where v is the final velocity (0 m/s), u is the initial velocity (500 m/s), and s is the stopping distance (0.25 m).

Substituting the values, we get a=-500000 m/s^2. Now, using F=ma, we get F=(500 kg)(-500000 m/s^2) = -250000000 N.

It is important to note that the negative sign indicates that the force is acting in the opposite direction of the initial velocity, as the gun is being stopped. This is why the magnitude of the force is half of what was calculated in the attempt.

I would also like to mention that it is important to always double check the units in the calculations to ensure that they are consistent and to use the correct equations for the given scenario.

## 1. What is the formula for calculating velocity of a gun and shell?

The formula for calculating velocity is velocity = distance / time. In the case of a gun and shell, the distance would be the length of the barrel and the time would be the time it takes for the shell to travel through the barrel.

## 2. How can the force of a gun and shell be calculated?

The force of a gun and shell can be calculated using the formula force = mass x acceleration. In this case, the mass would be the weight of the shell and the acceleration would be the change in velocity over time.

## 3. What factors can affect the velocity and force of a gun and shell?

The velocity and force of a gun and shell can be affected by several factors including the length and diameter of the barrel, the weight and shape of the shell, the type of gunpowder used, and external factors such as wind and temperature.

## 4. How is the velocity and force of a gun and shell measured in real-world scenarios?

The velocity and force of a gun and shell can be measured using specialized equipment such as chronographs and pressure sensors. These tools are used to capture data on the speed and force of the shell as it is fired from the gun.

## 5. Can the velocity and force of a gun and shell be controlled?

Yes, the velocity and force of a gun and shell can be controlled by adjusting various factors such as the length and diameter of the barrel, the type of gunpowder used, and the weight and shape of the shell. However, there are also external factors that may affect the velocity and force, such as wind and temperature, which may be more difficult to control.

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