An astronaut on the Moon attaches a small brass ball to a 1.00-m length of string and makes a simple pendulum. She times 15 complete swings in 75 seconds. From this measurement she calculates the acceleration due to gravity on the Moon. What is her result?

1.58 m/s².

Explanation:

The period of a simple pendulum is given as

T = 2π√(L/g) Equation 1

Where T = Period of the simple pendulum, L = Length of the simple pendulum, g = acceleration due to gravity.

make g the subject of the equation.

g = 4π²L/T² Equation 2

Given: L = 1.00 m, T = 75/15 = 5 seconds.

Constant: π = 3.14

Substitute into equation 2

g = 4(3.14)²(1)/5²

g = 1.58 m/s².

Thus her result = 1.58 m/s².