A laboratory uses a simple pendulum of nominal length 1.000m to generate a standard 2.000s time interval. The pendulum is mounted inside a lift (elevator) that may accelerate vertically.
(i) If the lift accelerates upward with magnitude a, write the expression for the effective gravitational acceleration g′ acting on the pendulum.
(ii) To ensure the time period remains exactly 2.000s for any acceleration in the range a=−2.0m s−2 (downward) to a=+2.0m s−2 (upward), derive an expression for the required pendulum length L′ in terms of g′.
(iii) Taking g=9.80m s−2 when the lift is at rest, calculate the maximum and minimum lengths that the adjustment mechanism must provide over the specified acceleration range.
(iv) Determine the percentage change in length relative to the nominal 1.000m that the mechanism must accommodate.