PHYS261 Final Review- Experiment 2
Suppose that your calipers are systematically reading inaccurately by consistently reporting lengths that are too short by 1%; i.e., when the calipers displays 10.00 mm the length is really only 10.10 mm. (a) Will your calculated density of the aluminum block be too high or too low compared to the real density? (b) By what percent will your calculated density be incorrect?
(a) The calculated density of the aluminum block would be too high compared to the actual density because the measured volume will be smaller compared to the actual volume. (b) 3%
Errors: Using the vernier calipers, estimate the uncertainty in a measurement of the length of a side of one of the blocks.
+- smallest unit of measurement, so in the calipers case this is +-0.1mm
Suppose you use the scale to measure the mass of the brass block. What is the uncertainty in the mass?
0.033 g
You measure the length of the same side of a block five times and find: b=11.0, 11.1, 11.2, 11.2, and 11.3 mm. What is the best estimate for b?
11.16 mm Take the average
Experiment 2 Purpose
To learn how to estimate uncertainty in measurements, how to do error propagation, and why it is important to understand the uncertainty in measurements
Using the ruler, and without using the vernier calipers, estimate how precisely you can measure the length of one of the sides of one of the blocks.
To within 0.5 mm or 0.25 mm
A block is measured to have a mass M = 25.3 g and volume V = 9.16 cm3 with an uncertainty of ∆M =0.05 g in the mass and ∆V =0.05 cm3 in the volume. What is the uncertainty in the density?
Use 2 eq's: 1. ro=M/V (to get density) 2. delta ro= ro×sqrt(delta M/M))^2+(delta V/V)^2) Means: Density=Mass/Volume Change in density= density × sqrt((Change in Mass/Mass)^2+(Change in Volume/Volume)^2) Answer: 0.016 g/cm^3
A block is measured to have a density ρ = 2.76 g/cm3 with an uncertainty of Δρ = 0.03 g/cm3. Find χ2 when the measured density is compared to the accepted density of pure aluminum ρ = 2.70 g/cm3.
Use Eq: Fancy x= (ro-ro knot)/delta(ro) Means: Fancy x= (measured density-accepted density)/(change in density) Answer here: 2
You measure the length of the same side of a block five times and each measurement has an uncertainty of ∆b = 0.1 mm. What is the uncertainty in the best estimate for b?
Use Eq: delta b/sqrt(number of times measured) 0.0447=0.10/sqrt(5)
