A non-relativistic particle of mass $m$ has momentum $p$ and kinetic energy $E_k$ - Edexcel - A-Level Physics - Question 8 - 2023 - Paper 4

For a non-relativistic particle, the kinetic energy is given by the formula:

$E_k = \frac{p^2}{2m}$

1. Calculate the momentum of the first particle:
   For the first particle:

   • Mass = $m$
   • Momentum = $p$
   • Kinetic Energy = $E_k$

2. Use the momentum to calculate the kinetic energy of the second particle:
   For the second particle:

   • Mass = $\frac{m}{2}$
   • Momentum = $2p$

   Substitute these values into the kinetic energy formula:

   $E_k = \frac{(2p)^2}{2 \left( \frac{m}{2} \right)} = \frac{4p^2}{m}$

3. Relate back to the kinetic energy of the first particle:
   From the first particle, we know: $E_k = \frac{p^2}{2m}$. Hence, we can express $p^2$ in terms of $E_k$: $p^2 = 2mE_k$.

4. Substitute $p^2$ into the second particle's kinetic energy equation:

   Therefore, substituting $p^2 = 2mE_k$ in: $E_k' = \frac{4(2mE_k)}{m} = 8E_k$.

Thus, the kinetic energy of the second particle is given by: Answer:
D: $8E_k$