Question

Sand is poured at a constant rate of 75.5 g/s into a 0.540-kg bucket resting on a scale. If sand is landing in the bucket with a speed of 3.70 m/s, determine the scale reading when there is 0.550 kg of sand in the bucket.

Answer 1

Answer:10.961 N

Explanation:

Given

mass flow rate in bucket is $\dot{m}=75.5 g/s$

mass of bucket $m=0.540 kg$

velocity of sand $v=3.70 m/s$

Force acting on bucket due to incoming of sand is given by

$F=\frac{\mathrm{d} m}{\mathrm{d} t}v$

$F=75.5\times 10^{-3}\times 3.7=279.35\times 10^{-3} N$

Now weight of sand and bucket when 0.55 kg sand is Present in bucket

$W_1=(0.54+0.55)\times 9.8$

$W_1=1.09\times 9.8=10.68 N$

Total reading on scale will be addition of weight and force acting by incoming sand

$Reading =10.68+0.279=10.961 N$