3. A physicist needs to estimate the density of a cube (all sides of the cube have equal length). Density (in kg/m³) can be found by M L3 where M is the mass of the object (in kg) and L is the length of a side of the cube (in meters). Assume the mass M~(μM = 1.0, 0 = 0.02²) (i.e. 1.0±0.02) and assume the length L~ (μL = 0.1, 0² = 0.0052) (i.e. 0.1±0.005). Assume M and L are independent. D = (a) Approximate μp. (b) Approximate op. (c) Write the estimate of the density, along with the estimated error, in engineering (i.e. ) notation. Be sure to state the units.
3. A physicist needs to estimate the density of a cube (all sides of the cube have equal length). Density (in kg/m³) can be found by M L3 where M is the mass of the object (in kg) and L is the length of a side of the cube (in meters). Assume the mass M~(μM = 1.0, 0 = 0.02²) (i.e. 1.0±0.02) and assume the length L~ (μL = 0.1, 0² = 0.0052) (i.e. 0.1±0.005). Assume M and L are independent. D = (a) Approximate μp. (b) Approximate op. (c) Write the estimate of the density, along with the estimated error, in engineering (i.e. ) notation. Be sure to state the units.
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A physicist needs to estimate the density of a cube (all sides of the cube have equal length). Density (in kg/m3)
can be found by D = M L3 where M is the mass of the object (in kg) and L is the length of a side of the cube (in meters). Assume the mass M ∼ ·(µM = 1.0, σ2 M = 0.022 ) (i.e. 1.0±0.02) and assume the length L ∼ ·(µL = 0.1, σ2 L = 0.0052 ) (i.e. 0.1±0.005).
Assume M and L are independent.
(a) Approximate µD.
(b) Approximate σD.
(c) Write the estimate of the density, along with the estimated error, in engineering (i.e. ±) notation. Be sure to
state the units.
Transcribed Image Text:3. A physicist needs to estimate the density of a cube (all sides of the cube have equal length). Density (in kg/m³)
can be found by
M
L³
where M is the mass of the object (in kg) and L is the length of a side of the cube (in meters). Assume the mass
M~(μm = 1.0, 0 = 0.02²) (i.e. 1.0±0.02) and assume the length L~ (μL = 0.1, o² = 0.005²) (i.e. 0.1±0.005).
Assume M and L are independent.
D=
(a) Approximate μp.
(b) Approximate op.
(c) Write the estimate of the density, along with the estimated error, in engineering (i.e. ) notation. Be sure to
state the units.
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