PL-1) Rachael and Ellie follow steps 1-6 of the procedure, measuring the mass of
ID: 1782972 • Letter: P
Question
PL-1) Rachael and Ellie follow steps 1-6 of the procedure, measuring the mass of the empty mass holder to be 66 g and the length of their pendulum to be 98.2 cm. Predict what the frequency of their pendulum will be in Hertz [Hint: convert to SI units before calculating]. PL-2) Ellie adds a 50 g mass to the mass holder. Predict the frequency of their pendulum in Hertz with the added mass. [As before, the mass holder has a mass of 66 g and the length of the pendulum is 98.2 cm]. PL-3) Rachael lets out some string so the total length of the pendulum is now 135.4 cm. Predict the frequency of their pendulum in Hertz with the longer string. [As before, the total mass of the pendulum is 66 g + 50 g.] PL-4) Rachael changes the length of the string again, and Ellie times the pendulum as it swings back and forth ten times, measuring 16.7 s. What is the frequency of their pendulum in Hertz? PL-5) Ellie and Rachael measure the acceleration due to gravity to be gave = 9.76 ± 0.05 N/kg. How does this compare to the accepted value of g? (A) It is numerically equal to g. (B) It is not numerically equal, but it is statistically equal to g, because of the standard deviation of the mean. (C) It is neither numerically nor statistically equal to g, because of the standard deviation of the mean. (D) We can’t tell from the information given. PL-1)=.503 PL-2)=.503 PL-3)=.428 PL-4)=.599 PL-5)= This is the question I need help with
Explanation / Answer
Solution:
Answer (PL-1): L = 98.2 cm = 0.982 m
Thus, f = [1/(2)](g/L) = [1/(2*3.14)](9.8/0.982) = 0.503 Hertz Answer (PL-1)
Answer (PL-2): As frequency of pendulum is independent of mass, thus, frequency will remain unchanged. Thus, f = 0.503 Hertz Answer (PL-2)
Answer (PL-3): L = 135.4 cm = 1.354 m
Thus, f = [1/(2)](g/L) = [1/(2*3.14)](9.8/1.354) = 0.428 Hertz Answer (PL-3)
Answer (PL-4): Time period, T = 16.7 s/10 = 1.67 s
Thus, f = 1/T = 1/1.67 s = 0.599 Hertz Answer (PL-4)
Answer (PL-5): Measured value of the acceleration due to gravity(g) = 9.76 ± 0.05 N/kg.
Accepted value of g = 9.81 N/Kg (which is not equal to measured value). Answer: Option (D) We can’t tell from the information given.
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