Question

A simple pendulum of length 1 feet suspended from the ceiling of an elevator takes π/3 seconds to complete one oscillation. Find the acceleration of the elevator

Answer 1

Answer ⇒ a = 4 ft/s².

Explanation ⇒ Given conditions,

Length of the pendulum = 1 feet.

Acceleration due to gravity(g) = 23 ft/s² [in FPS System.]

T = π/3

Using the formula,

$T = 2\pi  \sqrt{\frac{l}{g'} }$

g' means the effective acceleration. Effective because elevator is also moving. Let elevator is moving upward with acceleration a.

If elevator will be moving downward then our answer will come negative.

∴ π/3 =2π√(1/g')

√g' = 2 × 3

 g' = 36

∴ g + a = 36

∴ a = 4 ft/s².

Since, answer is not negative, this means our assumption was correct.

Hope it helps.

Answer 2

Answer:

Given conditions,

Length of the pendulum = 1 feet.

Acceleration due to gravity(g) = 23 ft/s² [in FPS System.]

T = π/3

Using the formula,

g' means the effective acceleration. Effective because elevator is also moving. Let elevator is moving upward with acceleration a.

If elevator will be moving downward then our answer will come negative.

∴ π/3 =2π√(1/g')

√g' = 2 × 3

 g' = 36

∴ g + a = 36

∴ a = 4 ft/s².

Since, answer is not negative, this means our assumption was correct.