Question

Sand is deposited at a uniform rate of 20 Kg/s and with negligible kinetic energy on to an empty conveyor belt moving horizontally at a constant speed of 10 meter per minute. Find (a) the force required to maintain the constant velocity, (b) the power required to maintain constant velocity, and (c) the rate of change of kinetic energy of the moving sand

Answer 1

$\frac{m}{t}=20\frac{kg}{s}$

$v=\frac{1}{6}\frac{m}{s}$

a) $F=ma=m\frac{v}{t}=\frac{m}{t}v$

$F=20*\frac{1}{6}=3.3$ N

b) $P=Fv=3.3*\frac{1}{6}=0.55$ Watts

c) $\frac{E}{t}=\frac{mv^2}{2t}=\frac{m}{t}\frac{v^2}{2}$

$\frac{E}{t}=20*\frac{1}{36*2}=0.28 \frac{J}{s}$