After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 55.0 cm. The explorer finds that the pendulum completes 108 full swing cycles in a time of 132 s. Part A What is the magnitude of the gravitational acceleration on this planet

The magnitude of the gravitational acceleration on this planet is 14.54 m/s².

Explanation:

given information:

pendulum length, L = 55 cm = 0.55 m

total swing, n = 108

time, t = 132 s

to calculate the gravitational acceleration of the planet, we can use the simple pendulum formula

T = 2π√ (L/g)

where

T = period (s)

L = the length of pendulum (m)

g = gravitational force (m/s²)

thus,

T² = (2π) ² (L/g)

g = (2π) ² (L/T²)

we know that

T = t/n

so,

g = (2π) ² (L/T²)

= (2π) ²[L / (t/n) ²]

= (2π) ²[L (n/t) ²]

= (2π) ² [0.55 (108/132) ²]

= 14.54 m/s²