A 0.540-kg bucket rests on a scale. Into this bucket you pour sand at the constant rate of 56.0 g/s. If the sand lands in the bucket with a speed of 3.20 m/s, (a) what is the reading of the scale when there is 0.750 kg of sand in the bucket? (b) What is the weight of the bucket and the 0.750 kg of sand?

a) 12.8212 N

b) 12.642 N

Explanation:

Mass of bucket = m = 0.54 kg

Rate of filling with sand = 56.0 g / sec = 0.056 kg/s

Speed of sand = 3.2 m/s

g = 9.8 m/sec2

Condition (a);

Mass of sand = Ms = 0.75 kg

So total mass becomes = bucket mass + sand mass = 0.54 + 0.75=1.29 kg

= = > total weight = 1.29 * 9.8 = 12.642 N

Now impact of sand = rate of filling * velocity = 0.056 * 3.2 = 0.1792 kg. m / sec2=0.1792 N

Scale reading is sum of impact of sand and weight force;

i-e

scale reading = 12.642 N+0.1792 N = 12.8212 N

Codition (b);

bucket mass + sand mass = 0.54 + 0.75=1.29 kg

==>weight = mg = 1.29 * 9.8 = 12.642 N (readily calculated above as well)