## Related questions with answers

Two carts move in the same direction along a frictionless air track, each acted on by the same constant force for a time interval $\Delta t$. Cart 2 has twice the mass of cart 1. Which one of the following statements is true? Cart 1 has the greater change in momentum.

Solution

Verified$\textbf{(b)}$ As we know the force acting on a body is defined as the change in momentum per unit time i.e.

$\begin{align*} \vec{F} = \frac{\Delta \vec{p}}{\Delta t}\tag{1} \end{align*}$

By rearranging the above equation (1), we get

$\begin{align*} \Delta \vec{p} = \vec{F}\,\Delta t \tag{2} \end{align*}$

Therefore the change in momentum of cart-1 is

$\begin{align*} \Delta \vec{p}_1 = \vec{F}_1\,\Delta t_1 \tag{3} \end{align*}$

And the change in momentum of cart-2 is

$\begin{align*} \Delta \vec{p}_2 = \vec{F}_2\,\Delta t_2 \tag{4} \end{align*}$

But here 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 from equations (3) and (4), we get

$\begin{align*} \Delta \vec{p}_1 = \Delta \vec{p}_2 \tag{5} \end{align*}$

Therefore the statement "Cart 1 has the greater change in momentum" is false.

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