Question

A truck of mass 500kg moving with constant speed 10m/s If sand is dropped into the truck at constant rate 10kg/min, the force required to maintain the motion with constant velocity is

Answer 1

m₀ = initial mass = 500 kg
v = velocity = 10 m/s
Δm = 10 kg/min = 1/6  kg/sec

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 = 1/6 kg * 10 m/s = 5/3 kg-m/s

Force additionally required = Δp/Δt = 5/3 Newtons

Answer 2

step-1

a=0 (moving with uniform velocity)
F =0

step-2

Rate of change of mass is 1/6 kg/sec.

Therefore after 1 sec. the mass will increase by 1/6 of initial mass.

The momentum required to keep the truck moving with 10m/sec. = 1/6kg × 10m/sec. =5/3 kg-m/sec. for 1 sec.

Therefore the force that is need to be applied = change in p / change in t

=5/3/1 N

=5/3 N