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Question

# 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

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$\textbf{(a)}$ 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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