Question:
a truck of mass 500kg is moving with constant speed10m/s .if sand is droped into the truck at constant rate.10kg/min ,the force is required to maintain the motion with constant velocity is
Answer:
The mass changes in this situation from (say) M0 to M0 + Δm
M₀ = Initial mass = 500 kg
v = velocity = 10 m/s
Δm = 10 kg/min = 10 / 60 = 1/6 kg/sec which means that in 1 sec 1/6Kg of load is added
The 500 kg truck is moving with uniform speed. So there is no force required to maintain its speed.
So in Δt = 1 sec. 1/6 kg of sand is added.
The momentum that is to be imparted to 1/6 kg of sand, so that it gains from 0 velocity to 10 m/s = Δp = Δm t = 1/6 kg * 10 m/s = 5/3 kg-m/s
Force additionally required = Δp/Δt = 5/3 Newtons
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