Answer:
F = 768 N
Explanation:
It is given that,
Speed of the elevator, v = 3.2 m/s
Grain drops into the car at the rate of 240 kg/min, [tex]\dfrac{dm}{dt}=240\ kg/min = 4\ kg/s[/tex]
We need to find the magnitude of force needed to keep the car moving constant speed. The relation between the momentum and the force is given by :
[tex]F=\dfrac{dp}{dt}[/tex]
[tex]F=m\dfrac{dv}{dt}+v\dfrac{dm}{dt}[/tex]
Since, the speed is constant,
[tex]F=m\dfrac{dv}{dt}[/tex]
[tex]F=v\dfrac{dm}{dt}[/tex]
[tex]F=3.2\times 240[/tex]
F = 768 N
So, the magnitude of force need to keep the car is 768 N. Hence, this is the required solution.
