The lab group has collected the following data. All +/- are absolute uncertainty
ID: 1532756 • Letter: T
Question
The lab group has collected the following data. All +/- are absolute uncertainty.
Voltage = 130.0 +/- 3.0 V.
Radius = 2.80 cm +/- 0.071 cm.
B = 1.35 x 10 -3 T +/- 0.01 x 10 -3 T.
A) Calculate the value for e/m to three significant digits using the formula e/m = 2V/(rB)2.
B) Calculate the fractional uncertainty for the voltage to two significant digits.
C) Calculate the fractional uncertainty for the radius to two significant digits.
D) Calculate the fractional uncertainty for B to two significant digits.
E) Calculate the fractional uncertainty for e/m to two significant digits..
Explanation / Answer
Given
Voltage = 130.0 +/- 3.0 V.
Radius = 2.80 cm +/- 0.071 cm.
B = 1.35 x 10 -3 T +/- 0.01 x 10 -3 T.
A)
e/m = 2V/(rB)2 ==> e/m = 2(130.0 +/- 3.0)/((2.80 cm +/- 0.071)(1.35 x 10 -3 T +/- 0.01 x 10 -3 ))^2
= (260 +/-6)/((0.028*0.00135) +/-(0.00071*0.00010))^2
= (260 +/-6)/((0.028*0.00135)^2 +/-(2*0.00071*0.00010))
= (260 +/-6)/(1.42884*10^-9 +/- 1.42*10^-7)
dividing
= (260/(1.42884*10^-9))+/-(6+1.42*10^-7)
= 181965790431.3989 +/- 6.000000142
= 181965790431.399 +/- 6
B) Calculate the fractional uncertainty for the voltage to two significant digits
Voltage = 130.0 +/- 3.0 V.
fractional uncertainity is = 3/130 = 0.023
C) Calculate the fractional uncertainty for the radius to two significant digits.
Radius = 2.80 cm +/- 0.071 cm.
fractional uncertainity is = 0.071/2.8= 0.03
D) Calculate the fractional uncertainty for B to two significant digits.
B = 1.35 x 10 -3 T +/- 0.01 x 10 -3 T.
fractional uncertainity is = (0.01*10^-3)/(1.35*10^-3)= 0.01
E) Calculate the fractional uncertainty for e/m to two significant digits
fractional uncertainity of e/m is
181965790431.399 +/- 6 = 6/(181965790431.399)= 3.297*10^-11
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