Gun and Shell: Calculate Velocity and Force

[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

Homework Equations

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??

 

[tiny-tim]

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)?

 

[Moetasim]

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.