Conservation of Momentum in Different Frames of Reference

[quantised]

Hello All,

The following may be a simple problem. But, your thoughts will be very much appreciated.

Homework Statement

Let's use a gun with mass m₁ and a bullet m₂. The bullet is fired in the positive direction with speed v₂, and the gun recoils in the negative direction with speed v₁.

Because the momentum is conserved, m₁v₁ = m₂v₂.

Hence, v₂ can be calculated if m₁, m₂ and v₁ are all known. In other words, v₂ = m₁v₁ / m₂. This calculation is from a stationary observer's frame of reference, outside the gun/bullet system.

Homework Equations

Now, I want to transform the same problem to the gun's frame of reference. (Hypothetically, it's an ant or a small person sitting at the muzzle observing the event!)

In this new frame of reference, the bullet moves at the following final speed: v_{b, final} = v₂ - v₁. The initial speed v_initial is zero, because the gun and the bullet are stationary. Therefore:

m₂ (v₂ - v₁) = (m₁ + m₂) v_initial = 0

This means that v₁ = v₂.

The Attempt at a Solution

Clearly, the answer from the first frame should be equal to the answer in the second frame.

Can someone please indicate to me where my working is incorrect?

Thanks in advance.

Quantised

 

[gneill]

The problem is that your chosen frame of reference is not an inertial frame -- it will experience an acceleration while the gun is being fired, which means there will be some transient pseudo forces operating on all objects measured from that frame. Physical laws (like conservation of momentum) do not apply without modification to non-inertial frames of reference.