Question

A. According to theory, the period T of a simple pendulum is T = 2????√ ???? ???? a. If ???? is measured as ???? = 1.40 ± 0.01 m, what is the predicted value of T?

b. Would you say that a measured value of T = 2.39 ± 0.01 ???? is consistent with the theoretical prediction of part (a)?

Answer 1

According to the theory of a simple pendulum, the period T is given by T = 2π√(l/g), where l is the length of the pendulum and g is the acceleration due to gravity. When l = 1.40 ± 0.01 m, the predicted value of T is 2.377 s. The measured value of T = 2.39 ± 0.01 s is consistent with the theoretical prediction.

Step-by-step explanation:

According to the theory of a simple pendulum, the period T is given by T = 2π√(l/g), where l is the length of the pendulum and g is the acceleration due to gravity.

To find the predicted value of T when l = 1.40 ± 0.01 m, we can substitute this value into the equation. The predicted value of T can be calculated as T = 2π√(l/g) = 2π√(1.40 / 9.8) = 2π√(0.1429) = 2π * 0.378 = 2.377 s.

For part b, the measured value of T = 2.39 ± 0.01 s is consistent with the predicted value of T = 2.377 s because the measured value falls within the range of the predicted value ± the uncertainty. Therefore, we can say that the measured value is consistent with the theoretical prediction.

Answer 2

a) T = (2,375 ± 0.008) s , b) When comparing this interval with the experimental value we see that it is within the possible theoretical values.

Step-by-step explanation:

a) The period of a simple pendulum is

T = 2π √ L / g

Let's calculate

T = 2π √1.40 / 9.8

T = 2.3748 s

The uncertainty of the period is

ΔT = dT / dL ΔL

ΔT = 2π ½ √g/L 1/g ΔL

ΔT = π/g √g/L ΔL

ΔT = π/9.8 √9.8/1.4 0.01

ΔT = 0.008 s

The result for the period is

T = (2,375 ± 0.008) s

b) the experimental measure was T = 2.39 s ± 0.01 s

The theoretical value is comprised in a range of [2,367, 2,387] when we approximate this measure according to the significant figures the interval remains [2,37, 2,39].

When comparing this interval with the experimental value we see that it is within the possible theoretical values.