Question

After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 53.0 cm. The explorer finds that the pendulum completes 109 full swing cycles in a time of 142 s

Answer 1

The period of the pendulum can be calculated using the formula:

T = (2π) * sqrt(L/g)

where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

Substituting the given values, we get:

T = (2π) * sqrt(0.53 m / g)

To find g, we can use the fact that the number of swing cycles in a given time is equal to the number of periods in that time. Therefore:

109 cycles = 54.5 periods (since one full cycle consists of two swings)

142 s = 54.5 * T

Substituting the value of T, we get:

142 s = 54.5 * (2π) * sqrt(0.53 m / g)

Solving for g, we get:

g = (4π^2 * 0.53 m) / (54.5)^2
g = 1.21 m/s^2

Substituting the value of g, we get:

T = (2π) * sqrt(0.53 m / 1.21 m/s^2)
T = 1.87 s

Therefore, the period of the pendulum is 1.87 s.