Use the rules in part e) of the review to combine the following numbers: L1 = 5.02 ± 0.03 m, L2 = 8.44 ± 0.06 m, t = 10.20 ± 0.04 s. Find the uncertainty of L1 + L2 and report the value of L1 + L2 Find the uncertainty of L1 × L2 and report the value of L1 × L2. c) Find the uncertainty of L1/t and report the value of L1/t. d) Find the uncertainty of L1 2 and report the value of L1 2 . In question 2(a) above, which value, L1 or L2, introduces the greater uncertainty to the value of L1 + L2 ? In question 2(c) above, which value, L1 or t, introduces the greater uncertainty to the value of L1/t ?
Question in bold!!
Use the rules in part e) of the review to combine the following numbers: L1 = 5.02 ± 0.03 m, L2 = 8.44 ± 0.06 m, t = 10.20 ± 0.04 s. Find the uncertainty of L1 + L2 and report the value of L1 + L2 Find the uncertainty of L1 × L2 and report the value of L1 × L2. c) Find the uncertainty of L1/t and report the value of L1/t. d) Find the uncertainty of L1 2 and report the value of L1 2 .
In question 2(a) above, which value, L1 or L2, introduces the greater uncertainty to the value of L1 + L2 ? In question 2(c) above, which value, L1 or t, introduces the greater uncertainty to the value of L1/t ?
Solution:
(a) Calculate the uncertainty of L1 + L2 as shown below.
∆(L1+L2)==±(0.03+0.06)±0.09 m∆L1+L2=±0.03+0.06=±0.09 m
Calculate the value of L1 + L2 as shown below.
L1+L2==(5.02+8.44)±0.09(13.46±0.09) mL1+L2=5.02+8.44±0.09=13.46±0.09 m
(b) Calculate the uncertainty of L1 x L2 as shown below.
∆(L1×L2)==±(0.03+0.06)±0.09 m∆L1×L2=±0.03+0.06=±0.09 m
Calculate the value of L1 x L2 as shown below.
L1×L2==(5.02×8.44)±0.09(42.37±0.09) mL1×L2=5.02×8.44±0.09=42.37±0.09 m
(c) Calculate the uncertainty of L1/t as shown below.
∆(L1t)==±(0.03+0.04)±0.07 m/s∆L1t=±0.03+0.04=±0.07 m/s
Calculate the value of L1/t as shown below.
L1t==(5.0210.2)±0.07(0.492±0.07) m/sL1t=5.0210.2±0.07=0.492±0.07 m/s
(d) Calculate the uncertainty of (L1)2L12 as shown below.
∆(L1)2==±(2×0.03)±0.06 m∆L12=±2×0.03=±0.06 m
Calculate the value of (L1)2L12 as shown below.
(L1)2==(5.022)±0.06(25.2±0.06) m
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