As shown in the figure, sand is falling from a stationary hopper onto a freight car which is moving with a uniform velocity v0=10m/s. The sand falls at the rate of μ=5kg/s. How much force is needed to keep the freight car moving at the speed v0?
A
50N
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
0N
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
25N
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
20N
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A50N As we know, thrust force acting on the car in the horizontal direction is given by Fth=μvr=(vrdmdt) Here, relative velocity of sand loading vr=−v0 i.e Fth=−μv0=−5×10=−50N (in opposite direction of velocity of car)
and thrust force acting in vertical direction Ftv=μv (Balanced by Normal force) where v is the velocity of sand falling into the car.
So we need, F=50N force in the direction of the car to move it with same speed).