Question

Five persons $A, B, C, D$ and $E$ are pulling a cart of mass $100 \,kg$ on a smooth surface and cart is moving with acceleration $3 \,m/s^{2}$ in east direction. When person A stops pulling, it moves with acceleration $1 \,m/s^{2}$ in the west direction. When person B stops pulling, it moves with acceleration $24 \,m/s^{2}$ in the north direction. What is the magnitude of acceleration in $(m/s^{2})$ of the cart when only $A$ and $B$ pull the cart keeping their directions same as the old directions?

Answer 1

When all are pulling
$\bar{F}_{\text{net}} =100\times3 \,\hat{i} \ldots\left(1\right)$
when A stops
$\bar{F}_{\text{net}}-\bar{F}_{A}=100\times1 \left(-\hat{i}\right) \ldots\left(2\right)$
when B stops
$\bar{F}_{net}-\bar{F}_{B}=100\times24\,\hat{j} \ldots\left(3\right)$
from these three get $\bar{F}_{A}+\bar{F}_{B}=\left(700 \hat{i}-2400\,\hat{j}\right)N$
hence acceleration of the cart
$\vec{a}=\frac{\bar{F}_{A}+\bar{F}_{B}}{m} = \frac{\left(700\,\hat{i}-2400\,\hat{j}\right)}{100} m /s^{2}$
$\vec{a}=\frac{\bar{F}_{A}+\bar{F}_{B}}{m}=\frac{\left(700 \hat{i}-2400\,\hat{j}\right)}{100} m /s^{2}$
$\vec{a} =\left(7 \hat{i}-24\,\hat{j}\right) m /s^{2}$
$\Rightarrow \left|\vec{a}\right|=\sqrt{7^{2}+24^{2}}=25 m /s^{2}$