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One way to measure the water content of a soil is to weigh
Chapter 3, Problem 6E(choose chapter or problem)
One way to measure the water content of a soil is to weigh the soil both before and after drying it in an oven. The water content is \(W=\left(M_{1}-M_{2}\right) / M_{1}\), where \(M_{1}\) is the mass before drying and \(M_{2}\) is the mass after drying. Assume that \(M_1=1.32\pm0.01\mathrm{\ kg}\) and \(M_2=1.04\pm0.01\mathrm{\ kg}\).
a. Estimate \(W\), and find the uncertainty in the estimate.
b. Which would provide a greater reduction in the uncertainty in \(W\): reducing the uncertainty in \(M_{1}\) to 0.005 kg or reducing the uncertainty in \(M_{2}\) to 0.005 kg?
Equation Transcription:
Text Transcription:
W = (M_1 - M_2)/M_1
M_1
M_2
M_1 = 1.32 pm 0.01 kg
M_2 = 1.04 pm 0.01 kg
W
Questions & Answers
QUESTION:
One way to measure the water content of a soil is to weigh the soil both before and after drying it in an oven. The water content is \(W=\left(M_{1}-M_{2}\right) / M_{1}\), where \(M_{1}\) is the mass before drying and \(M_{2}\) is the mass after drying. Assume that \(M_1=1.32\pm0.01\mathrm{\ kg}\) and \(M_2=1.04\pm0.01\mathrm{\ kg}\).
a. Estimate \(W\), and find the uncertainty in the estimate.
b. Which would provide a greater reduction in the uncertainty in \(W\): reducing the uncertainty in \(M_{1}\) to 0.005 kg or reducing the uncertainty in \(M_{2}\) to 0.005 kg?
Equation Transcription:
Text Transcription:
W = (M_1 - M_2)/M_1
M_1
M_2
M_1 = 1.32 pm 0.01 kg
M_2 = 1.04 pm 0.01 kg
W
ANSWER:Solution:
Step 1 of3:
To measure the water content of a soil weigh the soil both before and after drying it in an oven.the water content is W= (M1-M2)/M2. Here M1 is the mass before drying and M2 is the mass after drying.If M= 1.320.01 kg,and M= 1.04
0.01 kg.
We have to find
- The estimate of W, and the uncertainty in the estimate.
- Which would provide a greater reduction in W: reducing the uncertainty in M1 to 0.005kg or reducing the uncertainty in M2 to 0.005kg.