## Related questions with answers

For the situation described in the previous question, which cart experiences the greater change in kinetic energy? Each cart has the same change in kinetic energy.

Solution

Verified$\textbf{(a)}$ As we know the change in kinetic energy is defined as

$\begin{align*} \Delta KE = \frac{\Delta p^2}{2\,m}\tag{1} \end{align*}$

Therefore the change in kinetic energy of cart-1 is

$\begin{align*} \Delta KE_1 = \frac{\Delta p_1^2}{2\,m_1}\tag{2} \end{align*}$

And the change in kinetic energy of cart-2 is

$\begin{align*} \Delta KE_2 = \frac{\Delta p_2^2}{2\,m_2}\tag{3} \end{align*}$

But here in the previous question, given that the same constant force for a time interva $\Delta t$ is applied on both cart i.e. $\vec{F}_1 = \vec{F}_2 = \vec{F}$ and $\Delta t_1 = \Delta t_2 = \Delta t$. Therefore

$\begin{align*} \Delta \vec{p}_1 = \Delta \vec{p}_2 \tag{3} \end{align*}$

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