General Physics

Question

A grocery store sells 5-kg bags of rice. You purchase 10 bags in almost 3 months and weigh them each time. You obtain the following measurements:

Week 1 weight: 4.8 kg

Week 2 weight: 5.3 kg

Week 3 weight: 4.9 kg

Week 4 weight: 5.4 kg

Week 5 weight: 4.9 kg

Week 6 weight: 5.4 kg

Week 7 weight: 4.8 kg

Week 8 weight: 5.3 kg

Week 9 weight: 5.2 kg

Week 10 weight: 5.3 kg

Calculate the following:

average mass.

deviation mass.

absolute uncertainty.

relative uncertainty.

determination of uncertainty.

Answer 1

Average mass. M_av= Sum of masses/ number of weights µ=(4.8,5.3,4.9,5.4,4.9,5.4,4.8,5.3,5.2,5.3)/10=5.13 kg

Deviation mass. Deviation: the amount by which a single measurement differs from a fixed value such as the mean.  =0.237

Absolute uncertainty: As weight values are given in one decimal place, that means δ=0.05 kg (half of the scale =0.1 kg); or in statistical approach r= 2σ/(n)^0.5  =2*0.237  =0.15

Relative uncertainty: 0.05 kg/5 kg=0.01 or  0.15/5.0=0.03