Question

A container of mass $200\text{kg}$ is moving toward right by applying a constant horizontal force $100\text{N}$. Initial velocity of container is zero. Sand is falling in container with a constant rate of $1\text{kg/s}$ with the help of a fixed cone, as shown in the figure. Find the velocity of the container (in $\text{m/s}$) at $t=100\text{sec}$.

Answer 1

Given
Mass of containter $=200\text{kg}$
Force $F=100\text{N}$
$\frac{dm}{dt}=1\text{kg/s}$
$t=100\text{s}$
As we know that force is given by $F=v\frac{dm}{dt}$
$F=v$
using Newtons second law,
$100–F=ma$
$100-v=200\frac{dv}{dt}$
${\int }_0^t\frac{dt}{200}={\int }_0^t\frac{dv}{100-v}$
$v=100(1-e^{-t/200})$
At $t=100s$
$v=100(1-e^{-100/200})$
$v=39.34\text{m/s}$